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: |
||||||
|
||||||
|
||||||