13. -4 points GHCollig11 3 7064 A phone company charges $11 per month plus a nic

Question

13. -4 points GHCollig11 3 7064 A phone company charges $11 per month plus a nickel per call. (a) Find a rational function that expresses the average cost (x) of a call in a month when x calls were made. (Write your answer in terms of dollars) ) To the nearest tenth of a cent, find the average cost of a call in a month when 65 calls were made. t (a) to find a formula that gives the number of calls (x) that can be made for an average cost x. (Write your answer in terms of formula that gives the (e) Find the inverse of the function found in part dolars.) f-1(x) = (d) How many calls need to made for an average cost of 10e per call? calls

Explanation / Answer

(a).The charges of the phone company are $11 plus a nickel i.e. $ 0.05 per call. Thus, for x calls in a month, the cost would be 11+0.05x so that average cost per call would be f(x) = (11+0.05x)/x.
(b).If 65 calls are made in a month, then the average cost per call would be (11+65*0.05)/65 = $14.25/65 = $ 0.22( on rounding off to the nearest cent).
( c). Let y = f(x) = (11+0.05x)/x. They xy =11+0.05x or, xy-0.05x = 11 or, x(y-0.05) = 11 so that x = 11/(y-0.05). Now, on interchanging x and y, we get f-1(x) = 11/(x-0.05).
(d). If x = $ 0.10, then f-1(0.10) = 11/(0.10-0.05) = 11/0.05 = 220. Thus 220 calls can be made if the average cost per call is $ 0.10.

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