- 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.