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

Answer:

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

Step-by-step 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 $A = 20,000(0.85)^t$