An Exponential Function is a function of the form y = ab^{x}, where both a and b are greater than 0 and b is not equal to 1.

More About Exponential Function

Exponential Decay
Exponential decay occurs when a quantity decreases by the same proportion r in each time period t. If A_{0} is the initial amount, then the amount at time t is given by A = A_{0}(1 - r)^{t}, where r is called the decay rate, 0 < r="">< 1,and="" (1-r)="" is="" called="" the="" decay=""> Exponential Growth
Exponential growth occurs when a quantity increases by the same proportion r in each time period t. If A_{0} is the initial amount then the amount at time t is given by A = A_{0}(1 - r)^{t}, where r is called the growth rate, 0 < r="">< 1,="" and="" (1="" +="" r)="" is="" called="" the="" growth="" factor.="">

Video Examples: Introduction To Exponential Functions

Example of Exponential Function

y = 4.3(1.23)^{X} is an exponential function.

Solved Example on Exponential Function

Ques: Evaluate the exponential function y = 5(4)^{x} when x = 2.5. Round off the answer to the nearest hundredth.

Choices:

A. 160
B. 625
C. 140
D. 80.58
Correct Answer: A

Solution:

Step 1: y = 5(4)^{x} [Original exponential function.]
Step 2: y = 5(4)^{2.5 }[Replace x with 2.5.]
Step 3: 5(32) = 160 [Use Calculator.]

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.