Problema Solution
a new car costs $23,000.The value decreases by 15% each year. write and exponential decay model for the cars value. use the model to estimate the value after 3 years.
Answer provided by our tutors
Exponential decay can be modeled by the equation:
y = C(1 - r)^t, where C is initial amount, r is decay rate as decimal, t is time.
In our case we have:
C = $23,000
r = 0.15
y = 23,000(1 - 0.15)^t
y = 23,000*0.85^t
We find the value after 3 years by replacing the value for t = 3 years:
y = 23,000*0.85^3
y = $14,124.88
The value of the car after 3 year is estimated to be $14,124.88.