Question

write an exponential function to model the situation. the value of a car is $18000 and is depreciating at a rate of 12% per year. v(t) = .12(18000)^t; v(t) = .88(18000)^t; v(t) = 18000(.12)^t; v(t) = 18000(.88)^t

Explanation:

Step1: Recall depreciation formula

The general exponential depreciation function is $V(t) = P(1-r)^t$, where $P$ is initial value, $r$ is depreciation rate, $t$ is time in years.

Step2: Identify given values

$P = 18000$, $r = 0.12$. Calculate $1-r$:
$1 - 0.12 = 0.88$

Step3: Substitute into formula

Substitute $P$ and $0.88$ into the depreciation function.
$V(t) = 18000(0.88)^t$

Answer:

V(t) = 18000(.88)ᵗ