In the Principles and Standards for grades 6-8, the "Algebra" section (p. 229) poses the following problem. Quick-Talk advertises monthly cellular phone service for $0.50 a minute for the first 60 min but only $0.10 a minute for each minute thereafter. Quick-Talk charges for the exact amount of time used. Answer the following:
a. Make one graph showing the cost per minute as a function of number of minutes and the other showing the total cost for calls as a function of the number of minutes up to 100 min.
b. If you connect the points in the second graph in part (a), what kind of assumption needs to be made about the way the telephone company charges phone calls?
c. Why does the total cast for calls consist of two line segments? Why is one part steeper than the other?
d. The function representing the total cost for calls as a function of number of minutes talked can be represented by two equations. Write these equations.
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