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
○ y = 18(0.15)^x
○ y = 20.7(1.15)^x
○ y = 20.7(0.15)^x

Explanation:

Step1: Recall the compound - growth formula

The formula for compound growth is \(y = a(1 + r)^x\), where \(a\) is the initial amount, \(r\) is the growth rate as a decimal, and \(x\) is the number of time - periods.
Here, the initial value \(a=\$18\), and the growth rate \(r = 15\%=0.15\).

Step2: Substitute the values into the formula

Substituting \(a = 18\) and \(r=0.15\) into \(y=a(1 + r)^x\), we get \(y = 18(1+0.15)^x=18(1.15)^x\).

Answer:

A. \(y = 18(1.15)^x\)