The cost to ride the commutertrain in Chicagois. Commutershavethe optionof buyinga monthly
couponbookcosting that allowsthemto ride the train for on eachtrip. Is this a gooddeal for
someonewho commuteseveryday to and from workon the train?
Solution:
We can representthe cost of the two situations,usingthe linearequationsand the graphsas follows:
As before,we can find the pointof intersectionof the lines,or in this case,the break-evenvaluein termsof
days,by solvingthe equation:
So, eventhoughit costsmoreto beginwith,after daysthe cost of the couponbookpaysoff and from
that pointon, the cost is less than for thoseriderswho did not purchasethe couponbook.
Example7:Non-LinearModeling
The cost of disabilitybenefitsin the SocialSecurityprogramfor the years2000–2005can be modeledas
a quadraticfunction.The formula
indicatesthe numberof people , in millions,receivingDisabilityBenefits yearsafter 2000.In what year
did the greatestnumberof peoplereceivebenefits?How manypeoplereceivedbenefitsin that year?
Solution: