Since 2010, more Americans have made some purchases online rather than in "bricks and mortar" retail stores. The total e-commerce retail sales by food and beverage stores can be modeled by
\[
f(x)=0.67 e^{0.229 x} \quad 1 \leq x \leq 10
\]
where $x$ is the number of years since 2010 and $f(x)$ is in billions of dollars. (Source: U.S. Census Bureau).
a. What is the growth rate?
The growth rate is Number percent per year.
b. Determine the average rate of change on the interval $[2,8]$ and interpret. Round to nearest hundredth.
The average rate of change is Number
Interpretation: This means that from 2012 to 2018 the total e-commerce retail sales by food and beverage
Click for List at an average rate of Number billion dollars per year.

Step 1 ：The growth rate is given by the coefficient of \(x\) in the exponent of the exponential function. In this case, the growth rate is \(0.229\) or \(22.9\%\) per year.

Step 2 ：For the average rate of change on the interval \([2,8]\), we need to calculate the difference in the function values at \(x=8\) and \(x=2\) and divide by the difference in \(x\) values, which is \(8-2=6\).

Step 3 ：Calculate the function values at \(x=8\) and \(x=2\), then subtract the value at \(x=2\) from the value at \(x=8\), and divide the result by \(6\).

Step 4 ：The average rate of change is approximately \(0.52\) billion dollars per year.

Step 5 ：Interpretation: This means that from 2012 to 2018 the total e-commerce retail sales by food and beverage stores increased at an average rate of \(0.52\) billion dollars per year.

Step 6 ：\(\boxed{\text{The growth rate is } 22.9\% \text{ per year. The average rate of change on the interval } [2,8] \text{ is approximately } 0.52 \text{ billion dollars per year. This means that from 2012 to 2018 the total e-commerce retail sales by food and beverage stores increased at an average rate of } 0.52 \text{ billion dollars per year.}}\)