Exponential Function
Definition of Exponential Function

• 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.

Example of Exponential Function

• y = 4.3(1.23)^x is an exponential function.

More about Exponential Function

• Exponential Decay

Exponential decay occurs when a Quantity decreases by the same Proportion r in each time period t. If A₀ is the initial amount, then the amount at time t is given by A = A₀(1 - r)^t, where r is called the decay rate, 0 < r < 1, and (1 - r)  is called the decay factor.

• Exponential Growth

Exponential growth occurs when a Quantity increases by the same Proportion r in each time period t. If A₀ is the initial amount then the amount at time t is given by A = A₀(1 - r)^t, 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 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.]

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

• Click here for samples
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