Answer:
a) decay factor is b = 0.9
b) y = 20,000(0.9)^x
c) y = $10,629
Step-by-step explanation:
a) What is the decay factor for the value of the car?
The formula used to find the decay factor is
y = a(b)^x
where y = future value
a = current value
b = decay factor
x = time
The decay factor is: b = 1-r
We are given rate r = 10% or 0.1
b = 1 - 0.1
b = 0.9
So, decay factor is b = 0.9
b) Write an equation to model the car’s value.
Using the formula:
y = a(1-r)^x
y = 20,000(1-0.1)^x
y = 20,000(0.9)^x
c) Use your equation to determine the value of the car six years after Kelly purchased it.
y = 20,000(0.9)^x
We need to find value after 6 years, so x=6
y = 20,000(0.9)^6
y = 10,628.82
y = $10,629
