Exponential Decay Models
A real life quantity that decreases by a fixed percent each year can be
modeled by the following equation:
y  a(1  r ) t
a is the initial amount, r is the percent decrease expressed as a decimal and
t is the time (in years).
Example 1:
You buy a new car for $24,000. The value of the car, y, decreases by 16%
each year.
A.) Write an exponential decay model for the value of the car.
B.) Estimate the value of the car after 5 years.
C.) Estimate the value of the car after 10 years.
D.) Create a table for the depreciation of the car in Excel.
E.) Use Excel to estimate the age of the car when its value is
approximately $1000.
F.) Paste a graph of Value of Car vs. Age of Car below from Excel.
G.) Describe the graph in F.)
Exponential Decay Models
Example 2:
You buy a new computer for $2100. The value of the computer decreases by
about 40% annually.
1.) Write an exponential decay model for the value of the computer.
2.) Use the model to estimate the value of the computer after 3 years.
3.) Create a table for the depreciation of the computer in Excel.
4.) Use Excel to determine the age of the computer when its value is
approximately $180.
5.) Paste a graph of Value of Computer vs. Age of Computer below.
6.) Describe the graph in 5.)