The scatter plot and linear regression models for the yearly revenue of restaurants $(R)$ and supermarkets $(S)$ are given in the popup below. The revenue for restaurants can be modeled by the equation $R=13\mathrm{.}5n+170\mathrm{.}5,$ and for supermarkets can be modeled by the equation $S=5\mathrm{.}5n+235\mathrm{.}0,$ where $n$ is the number of years since $1986$ and revenue is in billions of dollars.

a$.$ Interpret the slope of each model.

b$.$ Use the model to predict the revenue of restaurants and the revenue of supermarkets in $2017.$

c$.$ Estimate the first year that restaurant revenue will exceed supermarket revenue by at least $150$ billion dollars.

Click the icon to view the scatter plot and data table of yearly revenue.

a$.$ Interpret the slope of each model.

The slope of the linear regression model for restaurants shows that the revenue is $($Type an integer or a decimal.$)$ at a rate of billion dollars per year.

The slope of the linear regression model for supermarkets shows that the revenue is

$($Type an integer or a decimal.$)$ at a rate of billion dollars per year.

b$.$ Use the model to predict the revenue of restaurants and the revenue of supermarkets in $2017.$

The predicted revenue for restaurants in $2017$ is billion dollars.

$($Type an integer or a decimal.$)$

The predicted revenue for supermarkets in $2017$ is billion dollars.

$($Type an integer or a decimal.$)$

c$.$ Estimate the first year that restaurant revenue will exceed supermarket revenue by at least $150$ billion dollars.

The first year that restaurant revenue will exceed supermarket revenue by at least $150$ billion dollars is $($Round up to the nearest year as needed.$)$