Question

A business purchases a computer for $3,000. The value of the computer decreases at a rate of 15% per year. Write an exponential function to model this situation. Then determine how much the computer will be worth after 4 years.

Answer 1

• The exponential function to model the decreasing value of the computer over time is V(t) = P * (1 - r)^t.
• The computer will be worth approximately $1,566.02, after 4 years.

How do we determine how much the computer will be worth after 4 years?

We can find how much the computer will be worth after 4 years using the formula above:

V(t) = P * (1 - r)^t

Where:

V(t) = the value of the computer after t years.

P = the initial purchase price of the computer ($3,000).

r = rate of decrease per year, (so for a 15% or 0.15 expressed as a decimal)

t = the time in years (t = 4)

Substituting these values into the formula:

V(t) = 3000 * (1 − 0.15)⁴

Next, we will find the value after 4 years :

V(4 ) = 3000 * (0.85)⁴

V(4 ) = 3000 * 0.52200625

V(4) = $1566.02

Hence, after 4 years, the computer will be worth approximately $1,566.02.