Exponential Models

Exponential Growth

P is the beginning amount (Principle)

r is the rate (percentage, written as a decimal)

t is time

(1+ r) is the growth rate

This amount will be more than 1

The base of our exponential function

Exponential Decay

P is the beginning amount (Principle)

r is the rate (percentage, written as a decimal)

t is time

(1- r) is the decay rate

This amount will be between 0 and 1

The base of our exponential function

Example 1

It costs $400 to buy a football autographed by Falcon’s quarterback Matt Ryan. It is expected increase in value 4% per year.

a) Does this equation represent growth or decay? _______________

b) What is the rate of growth or decay?_______________

c) What is the initial value? _______________

d) Write a model describing this situation. _______________

Example 2

A house in my neighborhood is for sale for $150,000. It is expected to increase in value 1.2% per year.

a) Does this equation represent growth or decay? _______________

b) What is the rate of growth or decay?_______________

c) What is the initial value? _______________

d) Write a model describing this situation. _______________

Example 3

A new I-Pad 2 costs $429. It is expected to decrease in value 15% each year.

a) Does this equation represent growth or decay? _______________

b) What is the rate of growth or decay?_______________

c) What is the initial value? _______________

d) Write a model describing this situation. _______________

Example 4

A brand new Chevy Camaro cost $29,000. It is expected to decrease in value 12% per year.

a) Does this equation represent growth or decay? _______________

b) What is the rate of growth or decay?_______________

c) What is the initial value? _______________

d) Write a model describing this situation. _______________