Exponential decay is a decrease by the same factor over equal time periods.
B
b
Exponential decay can be described using the equation y=ab^t where b is between 0 and 1.
C
c
Use the equation from Part A and substitute 4 for t.
D
d
Substitute 6000 for y and solve the resulting equation.
E
e
Substitute -2.7 for t.
A
a
See solution.
B
b
y=23 500(0.8)^t
C
c
About $9600
D
d
About 6.1 years
E
e
About $43 000
Practice makes perfect
a
This is an example of exponential decay. This means that the car's value can be described by an exponential function with a multiplier b that is between 0 and 1.
y=ab^x
Since the car decreases annually by 20 %, we have a multiplier of b= 0.8.
y=a( 0.8)^x
b
From Part A, we have already written half the function. We are only missing the initial value. In Part B, we have been given this value as a= 23 500.
y= 23 500(0.8)^t
c
By substituting t=4 into the function from Part B, we can determine the car's worth in four years.
Thus, approximately 6.1 years from now the car will be worth $6000.
e
When t=0, the car's value is $23 500. We want to know what the car was worth when it was new, which was 2.7 years ago. We can find that by substituting - 2.7 for t in the equation.
