Question

1. jack bought a new boat for $36,000. the value of the boat continuously depreciates at a rate of 15%. find the value of the boat after 5 years.

Explanation:

Step1: Recall continuous depreciation formula

The formula for continuous depreciation is $A = Pe^{-rt}$, where $P$ is the initial value, $r$ is the depreciation rate, $t$ is time in years, and $A$ is the final value.

Step2: Identify given values

$P = 36000$, $r = 0.15$, $t = 5$

Step3: Substitute values into formula

$A = 36000e^{-(0.15)(5)}$

Step4: Calculate exponent term

First compute $0.15 \times 5 = 0.75$, so $A = 36000e^{-0.75}$

Step5: Compute final value

$e^{-0.75} \approx 0.472367$, so $A \approx 36000 \times 0.472367$
$A \approx 17005.21$

Answer:

$\approx \$17,005.21$