This document provides an overview of exponential functions. Exponential functions have the form f(x)=bx, where b is the base and x is the exponent. The exponent is the variable. Exponential functions are important for modeling real-life situations like population growth. They start off slowly but increase very rapidly. To solve exponential equations, express both sides with the same base and set the exponents equal. For example, to solve 54-t=25t-1, write the right side as (5)2t-1 and set the exponents equal: 4-t=2t-1.

1. General Mathematics Chapter 3:
Exponential Functions
JANE CALMA

2. Exponential Functions
IS A MATHEMATICAL FUNCTION IN WHICH AN
INDEPENDENT VARIABLE APPEARS IN ONE OF
THE EXPONENTS —ALSO CALLED EXPONENTIAL.

3. why is it important?
The exponential function is very important in math
because it is used to model many real life situations
For example: population growth and decay, compound interest,
economics, and much more.

4. How is this function different
from functions that we have
worked with previously?
Definition of Exponential Function
f(x)=bX

5. How is this function different
from functions that we have
worked with previously?
THE EXPONENT IS THE VARIABLE!
Definition of Exponential Function
f(x)=b
x

6. f(x)=b
b = The base b >0 and b ≠ 1
x = The exponent x=any real number
Is f(x)=x an exponential function?
3
i
X

7. The Graph of an
Exponential Function
One of the most common
exponential functions is f(x)=2
x

8. f(x)=2x
The graph starts off slow but
then increases very rapidly
The x-axis (y=0) is an asymptote.
X can be any real number,
for example: f(x)2sqrt{3}
(0,1) is the y intercept

9. Solving Exponential Function
1.EXPRESS EACH SIDE OF THE EQUATION AS A POWER OF THE SAME BASE.
2.SET THE EXPONENTS EQUAL AND SOLVE.
3.CHECK YOUR ANSWER!
Main idea If the bases are the same,
set the exponents equal!

10. ALL WE HAVE HERE IS A SIMPLE ALGEBRA
PROBLEM
Let's look at some examples!
solve for x
7x-2
=73x
Are the bases equal?
Set the exponents equals. Solve for x.
x-2=3x
x=-1

11. Let's check
our Answer!
x=-1
7x-2=73x
7(-1)(-2)
=73(-1)
7-3=7-3

12. Let's check
our Answer!
x=-1
7x-2=73x
7(-1)(-2)
=73(-1)
7-3=7-3
It Checks!

13. Example #2
solve for x
54-t
=25t-1
Are the bases equal?
Change the right side to:
(5 )
2 t-1
Simplify: 54-t
=52t-2
Solved!t=2

14. Let's check our
Answer!
t=2
5
4-t
=25
t-1
5
4-2
=25
2-1
52
=251

15. Let's check our
Answer!
t=2
5
4-t
=25
t-1
5
4-2
=25
2-1
52
=251 It checks!

16. Exponential Function
EXPONENTIAL
FUNCTION
b= the base
b > o and b ≠ 1
x = the exponent
x = any real numbers
REVIEW!
f(x)=bx

17. Exponential Function
EXPONENTIAL
FUNCTION
b= the base
b > o and b ≠ 1
x = the exponent
x = any real numbers
an equation where the
exponents is the variable
REVIEW!
f(x)=bx
EXPONENTIAL
EQUATION

18. Exponential Function
EXPONENTIAL
FUNCTION
b= the base
b > o and b ≠ 1
x = the exponent
x = any real numbers
an equation where the
exponents is the variable
REVIEW!
f(x)=bx
EXPONENTIAL
EQUATION
EXPONENTIAL
FUNCTION
An exponential function is
a function of the
form f(x) = b
where b is a fixed positive number.
The constant b is called the
base of the exponent.
For example, f(x)=2x is an
exponential function with base
x

19. Thank you so much for
listening!
LOUIE JANE CALMA
STEM 11 - ST. PATRICK
@MOJUNGKOORI
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JANE CALMA
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