Question

Does anyone know the answers to this? I can’t figure it out

Answer 1

`y=57(0.88)^t`
`\text{ \$}20.50`

Step-by-step explanation:

An exponential decay function is generally given in the below;

`y=a\cdot(1-r)^t`

where a = initial amount

r = percentage rate of decrease in decimal

t = number of years

Given the initial value of the book(a) as $57 and the percent decrease(r) as 12% which as a decimal is 0.12 (12/100), let's go ahead and substitute these values into the above formula and we'll have;

`\begin{gathered} y=57(1-0.12)^t \\ y=57(0.88)^t \end{gathered}`

When t = 8, let's go ahead and solve for y;

`\begin{gathered} y=57(0.88)^8 \\ y=\text{ \$}20.50\text{ (to the nearest cent)} \end{gathered}`