Pergunta
18. Cộst The cost of renting tuxes for the Choral Society's for- mal is 20 down, plus 88 per tux. Express the cost C as a function of x, the number of tuxedos rented Use your func- tion to answer the following questions. a. What is the cost of renting 2 tuxes? b. What is the cost of the 2nd tux? c. What is the cost of the 4 ,098th tux? d. What is the variable cost? What is the fixed cost? What is the marginal cost? e. Graph C as a function of x.
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a. To find the cost of renting 2 tuxes, we can substitute x = 2 into the function C(x) = 20 + 88x.
C(2) = 20 + 88(2) = 20 + 176 = 196
So, the cost of renting 2 tuxes is 196. b. The cost of the 2nd tux is the difference between the cost of renting 2 tuxes and the cost of renting 1 tux. C(2) - C(1) = 196 - (20 + 88(1)) = 196 - 108 = 88 So, the cost of the 2nd tux is 88.
c. To find the cost of the 4,098th tux, we can substitute x = 4,098 into the function C(x) = 20 + 88x.
C(4,098) = 20 + 88(4,098) = 20 + 360,864 = 360,884
So, the cost of the 4,098th tux is 360,884. d. The variable cost is the cost that changes with the number of tuxes rented, which is 88 per tux. The fixed cost is the initial cost of renting the tuxes, which is 20. The marginal cost is the additional cost of renting one more tux, which is also 88.
e. To graph C as a function of x, we can plot the points (0, 20), (1, 108), (2, 196), (4,098, 360,884) and connect them with a straight line. The graph will be a straight line with a slope of 88 and a y-intercept of 20.
C(2) = 20 + 88(2) = 20 + 176 = 196
So, the cost of renting 2 tuxes is 196. b. The cost of the 2nd tux is the difference between the cost of renting 2 tuxes and the cost of renting 1 tux. C(2) - C(1) = 196 - (20 + 88(1)) = 196 - 108 = 88 So, the cost of the 2nd tux is 88.
c. To find the cost of the 4,098th tux, we can substitute x = 4,098 into the function C(x) = 20 + 88x.
C(4,098) = 20 + 88(4,098) = 20 + 360,864 = 360,884
So, the cost of the 4,098th tux is 360,884. d. The variable cost is the cost that changes with the number of tuxes rented, which is 88 per tux. The fixed cost is the initial cost of renting the tuxes, which is 20. The marginal cost is the additional cost of renting one more tux, which is also 88.
e. To graph C as a function of x, we can plot the points (0, 20), (1, 108), (2, 196), (4,098, 360,884) and connect them with a straight line. The graph will be a straight line with a slope of 88 and a y-intercept of 20.
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