Question

halstead, brayden unit 6 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 \(A = P(1 + r)^t\), where \(P\) is the initial amount, \(r\) is the growth rate (as a decimal), and \(t\) is the time.

Step2: Convert the percentage to a decimal

Given \(r=1.4\%=\frac{1.4}{100}=0.014\). The initial price \(P = 17.99\) and the time is \(x\) years.

Step3: Substitute into the formula

Substituting \(P = 17.99\), \(r = 0.014\) into \(A = P(1 + r)^t\), we get \(f(x)=17.99(1 + 0.014)^x=17.99(1.014)^x\).

Answer:

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