Question

Between 2005 and 2009, the average rate of inflation was about 4.8% per year. If a cart of groceries cost $110 in 2005, what did it cost in 2009?

Answer 1

`\bf \qquad \textit{Amount for Exponential change}\\\\ A=P(1\pm r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{starting amount}\to &110\\ r=rate\to 4.8\%\to (4.8)/(100)\to &0.048\\ t=\textit{elapsed period}\to &4\\ \end{cases} \\\\\\ A=110(1+0.048)^4`

the rate is positive, because is a rate of increase, from 2005 to 2009, is 4 years, 2005 being t = 0

Answer 2

(4.8/100)+1 = 1.048 (Making the multiplier)

110 * (1.048)^(2009-2005)

110 * (1.048)^(4) = 132.69

The cart of groceries would cost, in 2009, $132.69

Hope this helps! :)