Question

A $20,000 business computer depreciates at a rate of 15% per year. What equation would model the value of the computer?

Answer 1

`A = 20,000(0.85)^t`

Explanation:

We will use the formula for compound interest here

where
`A = p( 1 + r)^t`

A=future value for any sum

P=present value of the sum

r= yearly interest rate, it should be expressed in decimal

t=time period , it should be in years

______________________________

given in the problem

p = $20,000

r = 15% (in decimal 15/100 = 0.15)

t is the time for which equation is to be model to find future value p

since, rate is for depreciation we need to take negative value of rate as value for computer will decrease

thus

r = -0.15

using the above values in formula
`A = p( 1 + r)^t`

`A = p( 1 + r)^t\\A = 20,000(1 - 0.15)^t\\A = 20,000(0.85)^t`

Thus, model equation for the value of the computer is
`A = 20,000(0.85)^t`