This document provides a mathematical formula to calculate the sum of the sequence ((x - 5)^2)/x from x = 3 to 8. The approximate value of the calculated sum is 3.4464.
This document contains graphs of two functions. The first function is f(x) = 3x - 6, which is a linear function that increases from left to right across the x-axis. The second function is f(x) = 1/x + 3, which is a non-linear function that approaches positive infinity as x approaches 0 from both sides and is undefined at x = 0.
1. The document is about Taylor polynomials for the function x e^-x.
2. It gives the Taylor series expansion for x e^-x and lists the first 20 Taylor polynomials P1(x) through P20(x).
3. Readers are asked to graph the function x e^-x along with its Taylor polynomials of varying degrees to compare how well the polynomials approximate the original function.
This document discusses graphing absolute value functions. It provides examples of graphing various absolute value functions, including f(x)=|x|^2, f(x)=2|x|-1, f(x)=|x|^2-1, f(x)=3|x|^2-4, f(x)=|cos(x)|, f(x)=2|x|-3-1, and shows how to write a piecewise function definition for f(x)=|x|^2. The graphs are V-shaped and symmetric about the y-axis, with vertices at the points where the absolute value terms are equal to zero.
This document discusses how to sketch graphs resulting from transformations of basic parent functions, including horizontal and vertical stretches as well as translations. It provides examples of stretching and translating graphs of f(x) = x^2 and generalizes the effects of stretches and translations on basic parent functions. The document concludes with instructions on combining multiple transformations and an example problem determining the x-intercepts resulting from a composite transformation.
The document describes how to graph a function by making a table of x and f(x) values, determining where the function crosses the x-axis to find zeros, and estimating relative maximum and minimum points. It provides an example table with values for x from -4 to 5 and the corresponding f(x) values. There are zeros between x = -2 and -1, -1 and 0, 0 and 1, and 2 and 3. The relative maximum occurs at x = 0 and the relative minimum at x = 3.
This document provides instructions for graphing trigonometric transformations in 3 steps: 1) Determine the a, b, c, and d values from the function's factored form. 2) Draw the median position and amplitude. 3) Determine the period and mark points to graph the wave-like function. Examples graph y=3sin(2x)-1, f(x)=sin(1/2x+1), and f(x)=2cos(3x)-2.
This document contains two polynomial functions. The first function is the product of three linear factors (x+2), (x-3), and (x-5). The second function is the product of a linear factor (x+1) and the square of the linear factor (x-1).
This is a mathematical function that defines a parabola. The function is f(x) = -.3(x-13.2)^2, which describes a parabola that is opened downward, with a vertex at (13.2, 0).
This document contains graphs of two functions. The first function is f(x) = 3x - 6, which is a linear function that increases from left to right across the x-axis. The second function is f(x) = 1/x + 3, which is a non-linear function that approaches positive infinity as x approaches 0 from both sides and is undefined at x = 0.
1. The document is about Taylor polynomials for the function x e^-x.
2. It gives the Taylor series expansion for x e^-x and lists the first 20 Taylor polynomials P1(x) through P20(x).
3. Readers are asked to graph the function x e^-x along with its Taylor polynomials of varying degrees to compare how well the polynomials approximate the original function.
This document discusses graphing absolute value functions. It provides examples of graphing various absolute value functions, including f(x)=|x|^2, f(x)=2|x|-1, f(x)=|x|^2-1, f(x)=3|x|^2-4, f(x)=|cos(x)|, f(x)=2|x|-3-1, and shows how to write a piecewise function definition for f(x)=|x|^2. The graphs are V-shaped and symmetric about the y-axis, with vertices at the points where the absolute value terms are equal to zero.
This document discusses how to sketch graphs resulting from transformations of basic parent functions, including horizontal and vertical stretches as well as translations. It provides examples of stretching and translating graphs of f(x) = x^2 and generalizes the effects of stretches and translations on basic parent functions. The document concludes with instructions on combining multiple transformations and an example problem determining the x-intercepts resulting from a composite transformation.
The document describes how to graph a function by making a table of x and f(x) values, determining where the function crosses the x-axis to find zeros, and estimating relative maximum and minimum points. It provides an example table with values for x from -4 to 5 and the corresponding f(x) values. There are zeros between x = -2 and -1, -1 and 0, 0 and 1, and 2 and 3. The relative maximum occurs at x = 0 and the relative minimum at x = 3.
This document provides instructions for graphing trigonometric transformations in 3 steps: 1) Determine the a, b, c, and d values from the function's factored form. 2) Draw the median position and amplitude. 3) Determine the period and mark points to graph the wave-like function. Examples graph y=3sin(2x)-1, f(x)=sin(1/2x+1), and f(x)=2cos(3x)-2.
This document contains two polynomial functions. The first function is the product of three linear factors (x+2), (x-3), and (x-5). The second function is the product of a linear factor (x+1) and the square of the linear factor (x-1).
This is a mathematical function that defines a parabola. The function is f(x) = -.3(x-13.2)^2, which describes a parabola that is opened downward, with a vertex at (13.2, 0).
This document defines and lists several common parent functions including: constant, linear, quadratic, cubic, absolute value, greatest integer, square root, cube root, exponential, logarithmic, reciprocal, rational, and trigonometric functions. The parent functions are basic building blocks used to model real world phenomena through transformations and combinations.
This document provides examples for graphing reciprocals of functions. It explains that for reciprocals, smaller numbers on the x-axis become larger on the y-axis, and vice versa. An example graphs the reciprocal of f(x)=1/x^2. It notes that reciprocals can be written in the form f(x)=k/x+h, where k and h are determined from the original function. Further examples graph the reciprocals of f(x)=2/x+4 and f(x)=sin(x).
The document discusses curve sketching of polynomial functions. It explains that the appearance of a polynomial graph depends on whether the exponent is odd or even. It also notes that the maximum number of roots is equal to the degree of the polynomial function. The steps for sketching a polynomial graph are outlined as: 1) Find the y-intercept, 2) Find all roots, 3) Determine the sign over intervals defined by roots, and 4) Sketch the graph.
This document discusses various topics related to differential calculus including:
1. Envelopes and families of curves defined by equations of the form F(x,y,a)=0 where the parameter a defines each curve.
2. Asymptotes of curves, including vertical, horizontal, and oblique asymptotes.
3. Methods for finding the slopes and equations of asymptotes for algebraic curves, which involve putting the curve in terms of its highest degree terms and setting the results equal to 0.
4. Examples showing how to apply these methods to find the asymptotes of a specific algebraic curve.
The document provides instructions for graphing functions with reciprocals. It outlines six steps: 1) Find and sketch any vertical asymptotes where the denominator is zero. 2) Find and sketch any horizontal asymptotes based on the degrees of the numerator and denominator. 3) Find and plot the y-intercept by evaluating f(0). 4) Find the x-intercept by solving the numerator. 5) Use sign analysis to determine where the function is positive and negative. 6) Use smooth curves to complete the graph.
This document provides an introduction to quadratic functions. It defines the standard form of a quadratic function as f(x) = ax^2 + bx + c, and shows how to graph simple quadratic functions like f(x) = x^2 by creating a table of x and y-values. It also introduces key concepts for quadratic functions like domain, range, vertex, axis of symmetry, and maximum/minimum values.
Quadratic functions are functions that can be described by an equation in the form f(x)=ax^2+bx+c. Examples of quadratic functions include f(x) = -2x^2 + x - 1 and f(x) = x^2 + 3x + 2. Quadratic equations were used to describe the orbits of planets around the sun and allow observation of planetary motion. Structural engineers also use quadratic equations to design tall skyscrapers.
This document provides 28 examples of graphs of different types of rational functions. The rational functions shown include those of the form y=1/x, y=-1/x, y=(x+a)/(x+b), and others with variations in the numerator and denominator polynomials. Each example graphically depicts a different rational function to illustrate their key characteristics and behaviors.
1) Rational functions are quotients of two polynomial functions. The parent rational function is f(x) = 1/x.
2) Graphs of rational functions can have vertical asymptotes where the function is undefined, horizontal asymptotes as constant lines the function approaches, and sometimes slant asymptotes.
3) Vertical asymptotes occur where the denominator is zero. Horizontal asymptotes occur depending on the relative degrees of the numerator and denominator: if the numerator degree is less than the denominator degree the horizontal asymptote is y=0, if the degrees are equal the horizontal asymptote is the quotient, and if the numerator degree is greater there is no horizontal asymptote.
A quadratic function is a polynomial function of the form f(x)=ax^2+bx+c, where a cannot equal 0. It is a second degree polynomial with the highest exponent being 2. Setting a quadratic function equal to 0 produces a quadratic equation, whose solutions are the roots of the equation. Quadratic functions are commonly used to model real world phenomena like projectile motion or profit functions and appear in nature as parabolic shapes.
The document discusses how to graph a parabola by finding its axis of symmetry and turning point. The axis of symmetry is the line that cuts the parabola into two equal halves and passes through the turning point. To find the axis of symmetry, use the formula x=-b/2a where a and b are the coefficients of the quadratic equation. The turning point is found by substituting the axis of symmetry back into the original equation and is written as an ordered pair (x, y). An example parabola y=x^2+6x-2 is used to demonstrate finding its axis at x=3 and turning point of (3, 25).
This document provides an overview and 11 examples of factoring different forms of quadratic expressions, including expressions of the form (x +/- a)(x +/- b), (x +/- a)2, and (x + a)(x - a).
This document discusses rational functions and provides examples of representing rational functions through tables of values, graphs, and equations. It defines a rational function as a function of the form f(x) = p(x)/q(x) where p(x) and q(x) are polynomials and q(x) is not the zero function. Examples are given of using rational functions to model speed as a function of time for running a 100-meter dash and calculating winning percentages in a basketball league.
This document discusses graphing polynomials. Polynomials with zeros of even multiplicity will have a horizontal tangent line at that zero, while polynomials with zeros of odd multiplicity will cross the x-axis at that zero. For example, a polynomial with a zero of multiplicity 2 at x=1 will have a horizontal tangent line there, while a polynomial with a zero of multiplicity 1 at x=-2 will cross the x-axis at -2.
The document discusses how to find the axis of symmetry and turning point of a parabola. The axis of symmetry is the line that cuts the parabola into two equal halves and passes through the turning point. The formula to find the axis of symmetry is x=-b/2a. For the parabola y=x^2+6x-2, the axis of symmetry is x=3 and the turning point is (3,25). An example is then given to find the axis of symmetry and turning point of y=x^2-6x+8.
The document discusses graphing and analyzing various polynomial and rational functions. It provides instructions to graph functions such as f(x) = x5 - x, find turning points of functions like f(x) = x3 - 2x2 - 3x + 7 in the first quadrant, and state vertical asymptotes and turning points for functions including f(x) = x2 - 8x - 20. It also lists review questions 1, 3, 5, 6, 11, and 19 from Exercise 1.8.
The document contains 20 multiple choice questions about functions. The questions cover topics such as function graphs, intercepts, maximum and minimum values, and modeling real world scenarios using functions. They require calculating outputs, intercepts, areas, and applying properties of functions like composition, translation, and elimination rates over time.
This document contains 7 practice problems related to signals and systems concepts:
1) Evaluating complex expressions involving a complex number z = 2eiπ/3
2) Showing relationships involving the real and imaginary parts of a complex number z
3) Deriving Euler's formula relations involving cosine and sine of an angle
4) Expressing complex functions in polar form and plotting the results
5) Showing an identity involving a complex exponential
6) Sketching various time shifts and time scalings of a signal x(t)
7) Evaluating definite integrals involving exponential functions
This document discusses the key elements of a quadratic function f(x) = ax^2 + bx + c. It explains that:
1) The y-intercept is indicated by the c coefficient as (0,c)
2) The vertex is calculated as (-b/2a, f(-b/2a))
3) The axis of symmetry passes through the vertex and is the line x=-b/2a.
It provides an example of the quadratic function f(x)=x^2+2x-8 and graphs it to illustrate these elements.
The document defines a definite integral as the integral of a function over a bounded interval from a to b, written as ∫f(x)dx from a to b. This represents the area under the curve of the function f(x) between the bounds a and b. Several examples are provided of calculating definite integrals to find the area under curves over given intervals using the Fundamental Theorem of Calculus. It is noted that definite integrals cannot result in negative area values.
Lidiane Ferreira Roberto forneceu seus dados pessoais e profissionais em um currículo. Ela tem formação no ensino médio e cursos em gerência financeira, recepcionista de hotel, gerência de marketing e informática básica. Sua experiência inclui trabalhos como recepcionista em uma agência de turismo por 4 meses e como manicure e depiladora por 6 meses.
Este documento presenta el syllabus de la asignatura de Informática II de la carrera de Enfermería de la Universidad Técnica de Machala. El syllabus describe los objetivos, competencias, contenidos y metodología de la asignatura. La asignatura se divide en 4 unidades: Web Universitaria y Biblioteca, Google Apps, Hoja de Cálculo Avanzado y Seguridad Informática. El syllabus también incluye el programa detallado de actividades por unidades y temas con sus respectivas semanas de estudio.
This document defines and lists several common parent functions including: constant, linear, quadratic, cubic, absolute value, greatest integer, square root, cube root, exponential, logarithmic, reciprocal, rational, and trigonometric functions. The parent functions are basic building blocks used to model real world phenomena through transformations and combinations.
This document provides examples for graphing reciprocals of functions. It explains that for reciprocals, smaller numbers on the x-axis become larger on the y-axis, and vice versa. An example graphs the reciprocal of f(x)=1/x^2. It notes that reciprocals can be written in the form f(x)=k/x+h, where k and h are determined from the original function. Further examples graph the reciprocals of f(x)=2/x+4 and f(x)=sin(x).
The document discusses curve sketching of polynomial functions. It explains that the appearance of a polynomial graph depends on whether the exponent is odd or even. It also notes that the maximum number of roots is equal to the degree of the polynomial function. The steps for sketching a polynomial graph are outlined as: 1) Find the y-intercept, 2) Find all roots, 3) Determine the sign over intervals defined by roots, and 4) Sketch the graph.
This document discusses various topics related to differential calculus including:
1. Envelopes and families of curves defined by equations of the form F(x,y,a)=0 where the parameter a defines each curve.
2. Asymptotes of curves, including vertical, horizontal, and oblique asymptotes.
3. Methods for finding the slopes and equations of asymptotes for algebraic curves, which involve putting the curve in terms of its highest degree terms and setting the results equal to 0.
4. Examples showing how to apply these methods to find the asymptotes of a specific algebraic curve.
The document provides instructions for graphing functions with reciprocals. It outlines six steps: 1) Find and sketch any vertical asymptotes where the denominator is zero. 2) Find and sketch any horizontal asymptotes based on the degrees of the numerator and denominator. 3) Find and plot the y-intercept by evaluating f(0). 4) Find the x-intercept by solving the numerator. 5) Use sign analysis to determine where the function is positive and negative. 6) Use smooth curves to complete the graph.
This document provides an introduction to quadratic functions. It defines the standard form of a quadratic function as f(x) = ax^2 + bx + c, and shows how to graph simple quadratic functions like f(x) = x^2 by creating a table of x and y-values. It also introduces key concepts for quadratic functions like domain, range, vertex, axis of symmetry, and maximum/minimum values.
Quadratic functions are functions that can be described by an equation in the form f(x)=ax^2+bx+c. Examples of quadratic functions include f(x) = -2x^2 + x - 1 and f(x) = x^2 + 3x + 2. Quadratic equations were used to describe the orbits of planets around the sun and allow observation of planetary motion. Structural engineers also use quadratic equations to design tall skyscrapers.
This document provides 28 examples of graphs of different types of rational functions. The rational functions shown include those of the form y=1/x, y=-1/x, y=(x+a)/(x+b), and others with variations in the numerator and denominator polynomials. Each example graphically depicts a different rational function to illustrate their key characteristics and behaviors.
1) Rational functions are quotients of two polynomial functions. The parent rational function is f(x) = 1/x.
2) Graphs of rational functions can have vertical asymptotes where the function is undefined, horizontal asymptotes as constant lines the function approaches, and sometimes slant asymptotes.
3) Vertical asymptotes occur where the denominator is zero. Horizontal asymptotes occur depending on the relative degrees of the numerator and denominator: if the numerator degree is less than the denominator degree the horizontal asymptote is y=0, if the degrees are equal the horizontal asymptote is the quotient, and if the numerator degree is greater there is no horizontal asymptote.
A quadratic function is a polynomial function of the form f(x)=ax^2+bx+c, where a cannot equal 0. It is a second degree polynomial with the highest exponent being 2. Setting a quadratic function equal to 0 produces a quadratic equation, whose solutions are the roots of the equation. Quadratic functions are commonly used to model real world phenomena like projectile motion or profit functions and appear in nature as parabolic shapes.
The document discusses how to graph a parabola by finding its axis of symmetry and turning point. The axis of symmetry is the line that cuts the parabola into two equal halves and passes through the turning point. To find the axis of symmetry, use the formula x=-b/2a where a and b are the coefficients of the quadratic equation. The turning point is found by substituting the axis of symmetry back into the original equation and is written as an ordered pair (x, y). An example parabola y=x^2+6x-2 is used to demonstrate finding its axis at x=3 and turning point of (3, 25).
This document provides an overview and 11 examples of factoring different forms of quadratic expressions, including expressions of the form (x +/- a)(x +/- b), (x +/- a)2, and (x + a)(x - a).
This document discusses rational functions and provides examples of representing rational functions through tables of values, graphs, and equations. It defines a rational function as a function of the form f(x) = p(x)/q(x) where p(x) and q(x) are polynomials and q(x) is not the zero function. Examples are given of using rational functions to model speed as a function of time for running a 100-meter dash and calculating winning percentages in a basketball league.
This document discusses graphing polynomials. Polynomials with zeros of even multiplicity will have a horizontal tangent line at that zero, while polynomials with zeros of odd multiplicity will cross the x-axis at that zero. For example, a polynomial with a zero of multiplicity 2 at x=1 will have a horizontal tangent line there, while a polynomial with a zero of multiplicity 1 at x=-2 will cross the x-axis at -2.
The document discusses how to find the axis of symmetry and turning point of a parabola. The axis of symmetry is the line that cuts the parabola into two equal halves and passes through the turning point. The formula to find the axis of symmetry is x=-b/2a. For the parabola y=x^2+6x-2, the axis of symmetry is x=3 and the turning point is (3,25). An example is then given to find the axis of symmetry and turning point of y=x^2-6x+8.
The document discusses graphing and analyzing various polynomial and rational functions. It provides instructions to graph functions such as f(x) = x5 - x, find turning points of functions like f(x) = x3 - 2x2 - 3x + 7 in the first quadrant, and state vertical asymptotes and turning points for functions including f(x) = x2 - 8x - 20. It also lists review questions 1, 3, 5, 6, 11, and 19 from Exercise 1.8.
The document contains 20 multiple choice questions about functions. The questions cover topics such as function graphs, intercepts, maximum and minimum values, and modeling real world scenarios using functions. They require calculating outputs, intercepts, areas, and applying properties of functions like composition, translation, and elimination rates over time.
This document contains 7 practice problems related to signals and systems concepts:
1) Evaluating complex expressions involving a complex number z = 2eiπ/3
2) Showing relationships involving the real and imaginary parts of a complex number z
3) Deriving Euler's formula relations involving cosine and sine of an angle
4) Expressing complex functions in polar form and plotting the results
5) Showing an identity involving a complex exponential
6) Sketching various time shifts and time scalings of a signal x(t)
7) Evaluating definite integrals involving exponential functions
This document discusses the key elements of a quadratic function f(x) = ax^2 + bx + c. It explains that:
1) The y-intercept is indicated by the c coefficient as (0,c)
2) The vertex is calculated as (-b/2a, f(-b/2a))
3) The axis of symmetry passes through the vertex and is the line x=-b/2a.
It provides an example of the quadratic function f(x)=x^2+2x-8 and graphs it to illustrate these elements.
The document defines a definite integral as the integral of a function over a bounded interval from a to b, written as ∫f(x)dx from a to b. This represents the area under the curve of the function f(x) between the bounds a and b. Several examples are provided of calculating definite integrals to find the area under curves over given intervals using the Fundamental Theorem of Calculus. It is noted that definite integrals cannot result in negative area values.
Lidiane Ferreira Roberto forneceu seus dados pessoais e profissionais em um currículo. Ela tem formação no ensino médio e cursos em gerência financeira, recepcionista de hotel, gerência de marketing e informática básica. Sua experiência inclui trabalhos como recepcionista em uma agência de turismo por 4 meses e como manicure e depiladora por 6 meses.
Este documento presenta el syllabus de la asignatura de Informática II de la carrera de Enfermería de la Universidad Técnica de Machala. El syllabus describe los objetivos, competencias, contenidos y metodología de la asignatura. La asignatura se divide en 4 unidades: Web Universitaria y Biblioteca, Google Apps, Hoja de Cálculo Avanzado y Seguridad Informática. El syllabus también incluye el programa detallado de actividades por unidades y temas con sus respectivas semanas de estudio.
Este documento proporciona instrucciones sobre los pasos básicos de RCP, incluyendo evaluación de la escena, activación de emergencias, comprobación de pulso, ciclos de compresiones torácicas y ventilaciones, y técnicas para abrir la vía aérea. Se explican los roles de dos rescatistas para proporcionar RCP efectiva con compresiones constantes y ventilaciones adecuadas.
Este documento apresenta o calendário de abastecimento de água proposto para a região do Agreste Central de Pernambuco no mês de setembro de 2015, dividindo a região em 16 setores e definindo para cada um o período e a frequência do abastecimento, assim como os bairros atendidos.
Fatec Jundiaí realizou programação especial para calourosfatecjundiai
A Fatec Jundiaí realizou uma programação especial para receber os novos calouros no segundo semestre de 2015. A diretora apresentou a faculdade e explicou sobre o funcionamento do estágio e atividades. Coordenadores apresentaram as dependências da instituição. Uma caloura escolheu o curso de Logística por morar perto de empresas do setor e ter afinidade com exatas. Também foi explicado sobre o Desafio INOVA de modelo de negócios.
Este documento ofrece servicios de asesoría y resolución de ejercicios para apoyar el aprendizaje en materias como fundamentos de la administración. Incluye instrucciones para dos tareas relacionadas con el análisis de un caso de estudio sobre un dilema ético en una escuela.
El documento presenta los resultados académicos de 10 estudiantes con su nota promedio, condición y regalo. Muestra también datos de venta de 5 vehículos incluyendo precio, descuentos, pago total, máximo, mínimo y promedio.
1) O Código Penal brasileiro adota majoritariamente a teoria monista ou unitária para o concurso de agentes, na qual todos que contribuem para o crime são considerados autores e recebem a mesma punição.
2) Há exceção quando o co-autor tinha intenção de participar de crime menos grave, recebendo a pena deste crime aumentada até a metade se o resultado mais grave era previsível.
3) A participação consiste em atos que não são necessariamente para a prática do crime, como instigação ou auxílio, mas o part
Rogelio Romaní Flores' class schedule for the 2015 semester includes the following courses: Software Engineering III, Automation, Thesis I, Special Topics, Security and Systems Auditing, Communications Systems II, and Advanced Programming. His classes are scheduled between 7 AM and 9 PM on Mondays, Tuesdays, Wednesdays, Thursdays, and Fridays.
Somos expertos en sistemas de riego tecnificado en sus campos de cultivo o jardinería. nos puede encontrar ubicados en Loma Bonita, Oaxaca, México. y servimos en todo el sureste del país, incluyendo Veracruz. Oaxaca, Chiapas y Tabasco.
O documento fornece informações sobre inscrições na catequese da Paróquia de São José em Pinhal Novo, incluindo datas para inscrição, documentos necessários e taxa. Também detalha o compromisso dos pais e educadores com a participação regular das crianças na catequese.
Paulo José Monteiro Patrão é um jornalista e professor luso-brasileiro nascido em 1960. Ele possui licenciatura em Ciências da Comunicação e várias especializações em jornalismo, marketing, roteiro, fotojornalismo e edição de imagem. Fala fluentemente português, espanhol, francês e inglês e tem experiência em jornalismo, produção audiovisual, fotojornalismo e tradução.
This document describes the calculation of accelerations and velocities in an exercise where the initial velocity is 12,000 and the final velocity is 3,000. It shows that the acceleration is calculated as the minimum of 1/5 of the current velocity squared or the difference between the current and final velocities. This acceleration is then subtracted from the current velocity to calculate the next velocity, until the final velocity of 3,000 is reached after 5 iterations.
This document calculates the price (P) of a bond that has a face value of 5000, a coupon rate of 6% yielding an annual coupon of 300, and is currently trading at 92.5% of face value resulting in a current price of 4625. It further calculates that there are 15 days of accrued interest since the last coupon payment using the formula f=number of days/360. The final price of the bond is 4637.50, which is the sum of the current price and the accrued interest.
The document shows a mathematical calculation to determine an interest rate of 5% on a loan amount of 12,988 over 5 years where the principal is 3000 and the future value is 4,329.33.