# Science:Math Exam Resources/Courses/MATH102/December 2016/Question B 07 (a)

MATH102 December 2016
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### Question B 07 (a)

Each day 100,000 people use Vancouver’s public transit system. Translink estimates that 2000 of those people ride on transit without paying (called free riders). The number of free riders caught by Translink officers in any particular day is given by ${\displaystyle R(N)=2000(1-e^{-kN})}$ where ${\displaystyle k=1/500}$ and ${\displaystyle N}$ is the number of Translink officers on duty that day. Each officer on duty costs Translink 1000 dollars per day.

(a) The fine collected from each free rider caught is F dollars and Translink hires ${\displaystyle N}$ officers. Write the function ${\displaystyle I(N)}$ showing net revenue from fines and cost of hiring?

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