Exponential Functions

 

An exponential function can be described by an equation of the form:

y  = a^x , where a > 0 and a ≠ 1

 

Graph of Exponential function with a > 1:

 

Note: y values change little for small values of x, but increase quickly as values of x become greater.

 

Graph of Exponential function with 0 < a < 1:

 

Note: the value of y decreases less rapidly as x increases.

 

Exponential Growth:

 

The general equation for exponential growth is:

y = C(1 + r)^t 

 

where y represents the final amount, C is the initial amount, r is the rate of change in decimal format, and t is time.

 

Compound Interest:

 

A special case of exponential growth is compound interest. The equation is:

 

A = P( 1 + r/n)^nt

where A is the resulting amount of the investment, P is the initial amount of money invested, r is the annual rate of interest in decimal form, n is the number of times that the interest in compounded each year, and t is the number of years the money is invested.

 

Exponential Decay:

 

The general equation for exponential decay is:

y = C(1 - r)^t

 

where y represents the final amount, C is the initial amount, r is the rate of change in decimal format, and t is time.