Question

a country has an inflation rate of 1.4% per year, meaning the cost of items will grow at a rate of 1.4% each year. in 2013, a new dvd cost $17.99. let x be the number of years since 2013. which function models the price of a new dvd after x years? f(x)=17.99 + 1.014x f(x)=17.99 + 1.4x f(x)=17.99(1.4)^x f(x)=17.99(1.014)^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 \(a=\$17.99\) (the initial price of the DVD in 2013) and \(r = 1.4\%=0.014\) (the inflation rate).

Step3: Substitute the values into the formula

Substituting \(a = 17.99\) and \(r=0.014\) into \(y=a(1 + r)^x\), we get \(y = 17.99(1+0.014)^x=17.99(1.014)^x\).

Answer:

\(f(x)=17.99(1.014)^x\) (the fourth option)