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.

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

Given that the initial value \(a=\$18\) and the growth rate \(r = 15\%=0.15\).
Substituting these values into the compound - growth formula \(y=a(1 + r)^{x}\), we get \(y = 18(1+0.15)^{x}\).

Answer:

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