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 values

The initial value of the poster $a = 18$, the rate of increase $r=0.15$ (since 15% = 0.15), and the number of years is $x$.

Step3: Substitute values into formula

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

Answer:

$y = 18(1.15)^x$