Question

If a boat depreciates in value according to the simple interest formula Y=20,000(.92)^2 find the rate of decay. Write as a percentage!

Answer 1

Rate of Decay = 8%

Explanation:

The decay formula is:

`F=P(1-r)^t`

Where F is the final value (here, it is given as "Y")

P is the initial value (here, given as 20,000)

r is the rate of decay (what we need to find)

t is the time (given as 2)

Comparing both the equations:

`F=P(1-r)^t\\Y=20,000(0.92)^2`

We see that:

1 - r =0.92

We solve for "r":

1 - 0.92 = r

0.08 = r

The rate of decay is 0.08, as a percentage, we need to multiply by 100, so we have:

0.08 * 100 = 8%

Rate of Decay = 8%