Answer:
<em>It would take 5 years for the car to have a value of less than $25,000</em>
Step-by-step explanation:
<u>Exponential Decaying Model</u>
The exponential function is often used to model natural decaying processes, where the change is proportional to the actual quantity.
We have the initial value of a car is $40,000. Each year it depreciates by 10%.
Thus the first year its value is 90% of the initial value:
V1 = 90 * $40,000 / 100 = $36,000
By the second year its value is 90% of $36,000:
V2 = 90 * $36,000 / 100 = $32,400
Note the value for a year n is the original value multiplied by 90% (or 0.9) to the power of n:
To find the number of years needed to have a value of less than $25,000, we solve the equation:
Dividing by 40,000:
Taking logarithms:
n =4.5
We'll round up to n = 5
It would take 5 years for the car to have a value of less than $25,000