Chapter 3.2, Problem 17E

Reminder Round all answer to two decimal places unless otherwise indicated.

Currency Conversion The number $P$ of British pounds that you can get from a bank is a linear function of the number $D$ of American dollars you pay. An American tourist arriving at Heathrow airport in England went to a banking window at the airport and gave the teller $70$ American dollars. She received $46$ British pounds in exchange. In this exercise, assume that there is no service charge for exchanging currency.

a. What is the rate of change, or slope, of $P$ with respect to $D$? Explain in practical terms what this number means. (Note: You need two values to calculate a slope, but you were given only one. If you think about it, you know one other value. How many British pounds can you get for zero American dollars?)

b. A few days later, the American tourist went to a bank in Plymouth and exchange $130$ American dollars for British pounds. How many pounds did she receive?

c. Upon returning to the airport, she found that she found that she still had $\pounds 12.32$ in British currency in her purse. In preparation for the trip home, she exchanged that for American dollars. How much money, in American dollars, did she get?