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)

Answer 1

Option A

Explanation:

Took the test

Answer 2

`y=18(1.15)^x`

Explanation:

we know that

The equation of a exponential growth function is equal to

`y=a(1+r)^x`

where

y ---> the value of the poster

x ---> the number of years

r ---> is the growth rate of change

a ---> is the initial value

In this problem we have

`a=18\\r=15\%=15/100=0.15`

substitute

`y=18(1+0.15)^x`

therefore

`y=18(1.15)^x`

Examples

For x=5 years

`y=18(1.15)^5=\$36.20`

For x=8 years

`y=18(1.15)^8=\$55.06`

For x=10 years

`y=18(1.15)^(10) =\$72.82`