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.