Concept explainers
Applications
Cell phone bills A phone company charges
a. Find a rational function that expresses the average cost
b. To the nearest tenth of a cent, find the average cost of a call in a month when
c. Find the inverse of the function found in a part (a) to find a formula that gives the number of calls
d. How many calls need to be made for an average cost of
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College Algebra (MindTap Course List)
- An Epidemic Model A certain disease is contracted in a population at an average age of A0 if no one is immunized at birth. If q percent of the population is immunized at birth, then the average age at which the disease is contracted is A(q). One model gives the relation. A(q)=100A0100q a What value of q gives a pole for this rational function? b. Explain in practical terms what happens to A(q) when q is near the pole.arrow_forwardIf the graph of a rational function has a removablediscontinuity, what must be true of the functionalrule?arrow_forward13. Inventory The yearly inventory expense E, in dollar, of a car dealer is the function of number Q of automobiles ordered at a time from the manufacturer. A dealer who orders a only few automobiles at a time will have the expense of placing several orders, whereas if the order sizes are large then the dealer will have large inventory of unsold automobiles. For one dealer, the formula is, E=425Q2+8000Q So E is a rational function of Q. a. Make a graph of E versus Q covering order sizes upto 10. b. Explain in practical terms the behavior of the graph near the pole at Q=0. Hint: Keep in mind that there is a fixed cost of processing each order, regardless of the size of the orderarrow_forward
- A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t)=2t+1 , express the area burned as a function of time, t (minutes).arrow_forwardRational Function? Is y=x+1x2 is a rational function?arrow_forwardViewing Earth: Astronauts looking at Earth from a spacecraft can see only a portion of the surface. See figure 2.47. The fraction F of the surface of Earth that is visible at a height h, in kilometers, above the surface is given by the formula F=0.5hR+h Here R is the radius of Earth, about 6380 kilometers. for comparison, 1 kilometer is about 0.62 mile, and the moon is about 380,000 kilometers from Earth. a. Make a graph of F versus h covering heights up to 100,000 kilometers. b. A value of F equal to 0.25 means that 25, or one-quarter, of Earths surface is visible. At what height is this fraction visible? c. During one flight of a space shuttle, astronauts performed an extravehicular activity at a height of 280 kilometers. What fraction of the surface of Earth is visible at that height? d. Is the graph of F concave up or concave down? Explain your answer in practical terms. e. Determine the limiting value for F as the height h gets larger. Explain your answer in practical terms.arrow_forward
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