Question

You have purchased a mobile home for $20,000 which depreciates at 10% per year.

At the end of what year will the value of the mobile home be worth $14,580?
Use V(n)= 20,000(9/10)^n
to solve the problem.

Answer 1

C. Three

Explanation:

We want to solve the equation for n:

14,580 = 20,000(9/10)^n

14580/20000 = 729/1000 = (9/10)^n

(9/10)^3 = (9/10)^n . . . . . . write the left side as a cube

3 = n . . . . . . equate exponents

After year 3, the value will be $14,580.

_____

You can use logarithms to find n:

log(0.729) = n×log(0.9) . . . . . . taking the log of the 2nd line above

log(0.729)/log(0.9) = n = 3