Question

Marcos purchased a sail boat for $56,900. He anticipates each year the boat will decrease in value by 8.1% from the previous year. Write an exponential function that models the value in dollars of the boat x years after Marcus's purchase.

Answer 1

Answer:
`56,900\left( 0.919\right)^x`

Explanation:

Given

Marcos purchased a sailboat for
`\$56,900`

Each year the boat will decrease in value by
`8.1\%`

After 1 year it is

`\Rightarrow 56,900-56,900* 0.081\\\Rightarrow 56,900\left( 1-0.081\right)\\`

after another year it becomes

`\Rightarrow 56,900\left( 1-0.081\right)-56,900\left( 1-0.081\right)* 0.081\\\Rightarrow 56,900\left( 1-0.081\right)\cdot \left( 1-0.081\right)\\\Rightarrow 56,900\left( 1-0.081\right)^2`

After
`x` years it is

`\Rightarrow 56,900\left( 1-0.081\right)^x`

`\Rightarrow 56,900\left( 0.919\right)^x`