15. A manufacturer is predicting profit, P, inthousands of dollars, on the sale of x tonnesof fertilizer according to the equation600x – 15000P(x)x + 100a) Sketch a graph of this relation.b) Describe the predicted profit as sales increase.c) Compare the rates of change of the profit atsales of 100 t and 500 t of fertilizer.

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Answered: 15. A manufacturer is predicting…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Let G represent the number of gallons of gasoline left in a car’s tank after it has been driven m miles from a filling station where it was last filled. The table below gives se- lected values of these quantities: (a) What kind of function is G = G(m)? How can you tell? (b) Determine the slope of the line that connects the first point (40, 11) to the last point (200, 3) from the table above. Interpret what this number tells us about how this car uses gasoline. (c) Find the y-intercept of the line that connects the first point (40, 11) to the last point (200, 3) from the table above. Interpret what this number tells us about how this car uses gasoline.
The digital music industry has been growing steadily since the 2000s. The function h represents the percentage of music sales that are digital as a function of the number of years since 2002, t. 15.8182+49.91t h(t) = 17.0418+0.52t a) Determine (and state) the Vertical Intercept. Be sure to express as a point and round values to 2 decimal places. b) Explain the Vertical Intercept's meaning in the problem context. c) Determine (and state) the Horizontal Asymptote. Be sure to express your answer as a line and round values to 2 decimal places.
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3.) The revenue equation (in billions of dollars) for corn production in the United States is approximated by R(x)=0.016x² +1.034x+11.338 Where x is in billions of bushels. For example if you have 10 billion bushels, then x = 10. (Data from www.usda.gov) a.) Find the marginal revenue function b.) Find and interpret the marginal revenue for 15 billion bushels c.) Find and interpret the marginal revenue for 20 billion bushels
Sarah pays a flat rate plus a rate per minute for her phone plan as shown in the graph above. The cost of Sarah's phone plan, C(t), can be represented by which of the following functions? A: C(t) = -0.10t+25 B: C(t) = 0.10t+25 C: C(t) = 25(0.10)^t D: C(t) = 25(1+0.10)^t
Suppose the function C(x) = 0.005x^3 − 0.15x^2 + 3x + 210 gives the daily cost to run a plastic tub factory on a day when x plastic tubs are manufactured.a) Find the marginal cost function. b) Find the marginal cost when 100 tubs have been manufactured. Explain this value in a sentence. c) Find the average cost per tub if 200 tubs are manufactured. d) Find the marginal average cost function C'(x).
10. The number of male alates in an ant colony has been found to be approximately a linear function of the age of the colony, with a 5-year-old colony having 8.2 alates on average, and a 17-year-old colony having an average of 33.4 alates. Write the number of male alates ( y ) as a linear function of the age of the colony in years (t).
Suppose soda is on sale for $0.50 a can, and you have a coupon for $0.80 off your total purchase. Write a function rule for the cost of n cans of soda. A)c(n)=0.80n-0.50 B)c(n)=0.50n-0.80 C)c(n)=(0.50+n)-0.80 D)c(n)=(0.80+n)-0.50

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