Question

Amtrak's annual passenger revenue for the years 1985-1995 is modeled approximately by the formulaR= 60 x 11| +962after 1980. In what year was the passenger revenue $722 million? In the years_ and _, the passengers revenue was $722 million.

Answer 1

Given the model of the revenue, R, such that;

`\begin{gathered} R=-60|x-11|+962 \\ \\ x=\text{ number of years after 1980} \end{gathered}`

When the revenue is $722 million;

`\begin{gathered} R=722 \\ \\ 722=-60|x-11|+962 \end{gathered}`

Now, we would solve for x;

`\begin{gathered} 60|x-11|=962-722 \\ \\ 60|x-11|=240 \\ \\ |x-11|=(240)/(60) \\ \\ |x-11|=4 \end{gathered}`

Now, apply the absolute rule;

`\begin{gathered} x-11=4,x-11=-4 \\ \\ x=15,x=7 \end{gathered}`

Thus, in the years 1987 and 1995, the passenger revenue was $722 million.