# Answer to Question #894 in Algebra for Sarah

Question #894

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

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

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

Expert's answer

a. P = $8,500*(1-0.15)

b. P (t=2) = $8,500*0.85

c. $2000 = $8,500*0.85

0.85

t = ln(0.2353)/ln(0.85) = 8.9 years.

^{t}b. P (t=2) = $8,500*0.85

^{2}= $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.

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