Question

A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.) y = 18(1.15)x

Answer 1

`y = 18 * 1.15^x`

Explanation:

Given

`a = 18` --- initial

`r =15\%` -- rate

Value after a year = $20.70

Required

Expression to calculate its value after y years

This is calculated using:

`y = ab^x`

Where

`b=1 +r`

Substitute
`r =15\%` in
`b=1 +r`

`b = 1 + 15\%`

`b = 1 + 0.15`

`b = 1.15`

Substitute
`b = 1.15` and
`a = 18` in
`y = ab^x`

`y = 18 * 1.15^x`