The document contains various mathematical problems and equations covering topics such as logarithms, exponential functions, systems of equations, and applications of these concepts in real-world scenarios. It includes evaluations, transformations between logarithmic and exponential forms, and application of compound interest formulas. Additionally, the document discusses properties of logarithms, graph selections, and systems of equations with practical examples.

1. 1.
Evaluate the function at the indicated value of x. Round your
result to three decimal places.
Function: f(x) = 0.5^x Value: x = 1.7
-0.308
1.7
0.308
0.5
2.
Solve for x. 3x = 81
7
3
4
-3
3.
Logarithms are the inverse of exponentials.

2. True
False
4.
The Logarithm Quotient Rule states:
logb(x / y) = logb(x) + logb(y)
logb(x / y) = logb(x) - logb(y)
logb(x y) = y ∙ logb(x)
logb(c) = 1 / logc(b)
5.
Use the properties of logarithms to expand the expression as a
sum, difference, and/or constant multiple of logarithms. Assume
all variables are positive.
log3 9x
log3 9 * log3 x
log3 9 + log3 x

3. log3 9 - log3
none of these
6.
Select the graph of the function. Indicate which graph is
correct: 1st, 2nd, 3rd, or 4th
f(x) = 5x-1
7.
Evaluate the function at the indicated value of x. Round your
result to three decimal places.
Value: x=2
8.
The exponential equation y=bx is equivalent to the logarithmic
equation x=logby
True
False
9.
Use the One-to-One property to solve the equation for x.
e(3x+5) = e6
x = -1/3
x2 = 6
x = 1/3

4. x = 3
10.
Write the logarithmic equation in exponential form.
log8 64 = 2
82 = 16
82 = 88
82 = 64
864 = 2
11.
Write the exponential equation in logarithmic form.
43 = 64
log64 4 = 3
log4 64 = 3
log4 64 = -3

5. log4 3 = 64
12.
The given x-value is a solution (or an approximate solution) of
the equation.
42x-7 = 16
x = 5
True
False
13.
Find the magnitude R of each earthquake of intensity I (let
I0=1). (Hint: R=log (I/I0)
I = 19000
3.28
5.28
4.28
2.38

6. 14.
pH is a measure of the hydrogen ion concentration of a solution.
It is defined as the negative logarithm of the hydrogen ion
concentration. The equation is:
pH = - log [H+]
If an acid has an H+ concentration of 10-4, what's the pH?
15.
A general formula for exponential Growth can be given by:
A = P ekt
In your textbook, or using another reliable source, research
what values, P, A, k and t represent and write your answer.
(Hint: What do each of the variables stand for?)
16.
Continuously compounded interest means your principal is
earning interest and you keep earning interest on the interest
earned. Research the formula for Continuously Compounded
Interest and write it below.
17.
$2500 is invested in an account at interest rate r, compounded
continuously. Find the time required for the amount to double.
(Approximate the result to two decimal places.)
r = 0.0570
13.16 years
10.16 years
11.16 years

7. 12.16 years
18.
Write Eulers Number (e) to three decimal places.
19.
Exponential functions often involve the rate of increase or
decrease of something such as a population, for example. If
there is a population increase, it is a _______ function and
when there is a decrease, it is a ________ function.
20.
Do some research on important numbers in mathematics. Choose
one that is interesting to you (it can be on e or pi or a different
number)
In your post, share with us what you have found out about the
number, for example, its history, some trivial facts about the
number, and/or how it is applied.
21.
A system of equations:
Has two or more equations with the same set of unknowns
Has one equation and two unknowns
Has two equations with different sets of unknowns

8. Has more sets of unknowns than equations
22.
A system of two linear equations and two unknowns can be
solved by:
Elimination
Substitution
Graphing the equations
All of the above
23.
A system of two linear equations and three unknowns can be
solved by:
Elimination
Substitution
Graphing the equations
It cannot be solved

9. 24.
A system of equations has as many equations as there are
variables (unknowns).
True
False
25.
Solve these two equations by elimination, substitution or
graphing
Equation 1: x+y=1
Equation 2: -2x+4y=6
X=-1/3, y = 4/3
X= 4/3, y = -1/3
X=1/3, y=4/3
X=-4/3, y-=1/3
26.
For the following System of Equations, the Matrix Form
included below is correct.
2x+y+z=4
6y+5z=-33x
5y-z=27
Matrix Form:
True

10. False
27.
The cost C (in millions of dollars) of removing p% of the
industrial and municipal pollutants discharged into a river is
given by
According to this model, explain why or why not it is possible
to remove 100% of the pollutants?
28.
The admission fee at the county fair is $2 for children
and $4 for adults. On a certain day, 2000 people enter the fair
and $5000 is collected. Using c as the variable to represent the
number of children and aas the variable for adults, write a
system of equations to determine how many children and how
many adults attended. Note down this system of equations so
that you can use it for the next question.
29.
Based on the system of equations you wrote in the previous
problem, how many children attended the county fair that day?
30.
Evaluate the function ƒ(x) = 5x + 4 at ƒ(0)
9
1
4

11. 0
31.
The profit P (in hundreds of dollars) that a company makes
depends on the amount x (in hundreds of dollars) the company
spends on advertising according to the model. P(x) = 230 + 40x
- 0.5x2 What expenditure for advertising will yield a maximum
profit?
40
0.5
230
20
32.
The concentration C (in mg/dl), of a certain antibiotic in a
patient's bloodstream is given by 50t/t^2+25 where t is the time
(in hours) after taking the antibiotic. What is the concentration
10 hours after taking the antibiotic?
33.
Write the logarithmic equation in exponential form.
Log2 16 = 4
34.
Find the domain of the function:

12. All real numbers
All real numbers except x=3
All positive real numbers
All real numbers except x=0
35.
pH is a measure of the hydrogen ion concentration of a solution.
It is defined as the negative logarithm of the hydrogen ion
concentration. The equation is:
pH = - log [H+]
If an acid has anH+ concentration of 10-7, find the pH?
36.
In order to join a movie streaming service, you pay a $75 annual
fee, then $1.50 for each movie you stream. Which equation will
allow you to determine the cost you will pay if you stream x
number of movies? Select from the following equations and
indicate the correct answer in the space below: 1st, 2nd, 3rd, or
4th.
37.
Evaluate the function at the indicated value of x.
Function: f(x) = 0.5x Value: x = 2
38.
Find the domain of the function

13. Domain: all real numbers x except x=7
Domain: all real numbers x except x=6
Domain: all real numbers x
Domain: all real numbers x except x = -6
39.
Express the following matrix as a system of equations:
40.
Solve for x.
4x = 16