8. if a boat depreciates in value according to the simple - interest formula $y = 20000(0.92)^t$, find the…
8. if a boat depreciates in value according to the simple - interest formula $y = 20000(0.92)^t$, find the rate of decay. show your work and write your answer as a percentage. (20 points)
Answer
Explanation:
Step1: Recall the general form of exponential decay
The general form of exponential decay is $y = a(1 - r)^t$, where $a$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. In the given formula $y = 20000(0.92)^t$, we can compare it with the general form.
Step2: Identify the rate of decay
We have $(1 - r)=0.92$. Solving for $r$, we get $r = 1 - 0.92$. $r=1 - 0.92=0.08$
Answer:
8%