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 compound - growth formula

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

Step2: Identify the initial amount and growth rate

The initial value of the poster $a=\$18$, and the growth rate $r = 0.15$ (since 15%=0.15).

Step3: Substitute values into the formula

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

Answer:

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