2.1 Exponential Growth: Worked Examples

Example 1.    Write a formula for an exponential function with initial value of 2,200 and a growth factor of 1.5.

SOLUTION.   The general exponential function is of the form , with C as the initial value and a as the growth factor, so the function is given by

Example 2.    Write a formula for an exponential function with initial value of 10,000 and doubling every time period.

SOLUTION.   Since the initial value is doubling every time period, the growth rate is 100% and the growth factor is . The function is given by

Example 3.    How much money would be in an account after 25 years if you deposited $5,000 at each of the following interest rates compounded monthly    

SOLUTION.  

a)     

b)     

c)     

d)     

Example 4.    How much money would be in an account after 25 years if you deposited $5,000 in a mutual fund which compounds interests 11%

SOLUTION.  

a)     

b)     

c)     

d)     

e)     

Example 5.    Find the effective annual yield for an account that gives 7.45% nominal interest compounded quarterly.

SOLUTION.   Use the compound interest formula for t = 1 and P = 1:

Subtract 1 and change the decimal to a percent:

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