Question

question 8 (multiple choice worth 1 points) (05.01h mc) if a new boat was purchased for $45,000, and the value of the boat decays continuously at a rate of 8% per year, what is the value of the boat after 7 years? use the formula $a(t)=ce^{rt}$
$25,704.41
$25,103.10
$19,800.00
$78,780.28

Explanation:

Step1: Identify given values

$c = 45000$, $r = -0.08$, $t = 7$

Step2: Substitute into decay formula

$A(7) = 45000e^{(-0.08)(7)}$

Step3: Calculate exponent term

$(-0.08)(7) = -0.56$, so $e^{-0.56} \approx 0.5712$

Step4: Compute final value

$A(7) = 45000 \times 0.5712 \approx 25704.41$

Answer:

$25,704.41$