Answer to Question #894 in Algebra for Sarah

Question

The value of some computer equipment depreciates at a rate of 15% for every year after its initial purchase. The initial cost of the equipment was $8,500

a. Write an exponential function that will give the value of the equipment at any time t, where t is in years.
b. How much will the computer equipment be worth in 2 years?
c. How long will it take for the computer equipment to have a value of $2000?

Answer 1

a. P = $8,500*(1-0.15)^t
b. P (t=2) = $8,500*0.85² = $6,141.25;
c. $2000 = $8,500*0.85^t;
0.85^t = 0.2353;
t = ln(0.2353)/ln(0.85) = 8.9 years.