8. if a boat depreciates in value according to the simple interest formula y = 20000(0.92)^t, find the rate…

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)\n\nstep 1: recall 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.\n\nstep 2: identify the rate of decay\nwe have (1 - r) = 0.92.

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)\n\nstep 1: recall 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.\n\nstep 2: identify the rate of decay\nwe have (1 - r) = 0.92.

Answer

Explanation:

Step1: Recall decay - formula comparison

The general exponential - decay formula is $y = a(1 - r)^t$. Given $y = 20000(0.92)^t$, we compare the two formulas.

Step2: Solve for the rate of decay

Set $1 - r=0.92$. Then, we can solve for $r$ by subtracting $0.92$ from $1$. So, $r = 1 - 0.92=0.08$.

Step3: Convert to percentage

To convert $r$ to a percentage, we multiply by $100$. So, $r = 0.08\times100 = 8%$.

Answer:

$8%$