Exponential Function
Definition of Exponential Function
- An exponential function is a function of the form
where a and b are both > 0 and b is not equal to 1.
Examples of Exponential Function
is an exponential function.
More about Exponential Function
Exponential decay occurs when a quantity decreases by the same proportion r in each time period t. If
is the initial amount then the amount at time t is given by
, where r is called the decay rate, 0 < r < 1, and
(1 - r) is called the decay factor.
Exponential growth occurs when a quantity increases by the same proportion r in each time period t. If is the initial amount then the amount at time t is given by
, where r is called the growth rate,
0 < r < 1, and (1 + r) is called the growth factor.
Solved Example on Exponential Function
Evaluate the exponential function 
when x = 2.5. Round the answer to the nearest hundredth.
Choices:
A. 160
B. 625
C. 140
D. 80.58
Correct Answer: A
Solution:
Step 1: [Original exponential function.]
Step 2: 
[Replace x with 2.5.]
Step 3: 5(32) = 160 [Use Calculator.]
Related Terms for Exponential Function
- Function
- Exponential Growth
- Exponential Decay
- Proportion
- Growth Factor
- Decay Factor
Real-world Connections for Exponential Function
- Exponential functions are used in banking and finance to calculate compound interest.
- Radioactive decay, population growth - these can be modeled using exponential functions.
Additional Links for Exponential Function
