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 rate of growth as a decimal, and \(x\) is the number of time periods.

Step2: Identify the values of \(a\) and \(r\)

Given that the initial value \(a=\$18\), and the rate of increase \(r = 15\%=0.15\).
Substituting \(a = 18\) and \(r = 0.15\) into the formula \(y=a(1 + r)^x\), we get \(y=18(1 + 0.15)^x\).

Answer:

\(y = 18(1.15)^x\) (the first option)