Question

a limited - edition poster increases in value each year with an initial value of $18. after 1 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)
$y = 18(1.15)^x$
$y = 18(0.15)^x$
$y = 20.7(1.15)^x$

Explanation:

Step1: Recall exponential growth formula

The general exponential growth formula is $y = a(1+r)^x$, where $a$ is the initial value, $r$ is the annual growth rate, and $x$ is the number of years.

Step2: Plug in given values

Initial value $a = 18$, growth rate $r = 0.15$. Substitute into the formula:
$y = 18(1+0.15)^x = 18(1.15)^x$

Step3: Verify with 1-year value

Calculate value after 1 year: $y = 18(1.15)^1 = 20.70$, which matches the given value.

Answer:

$y = 18(1.15)^x$