The demand for a new computer game can be modeled by p(x)=59-4ln(x),where p(x) is the price consumers will pay, in dollars and x is the number ofgames sold, in thousands. Recall that total revenue is given by R(x) = x·p(x)a) Find the marginal revenue, R'(x).b) How many games will be sold if the price is $47?KA

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Answered: The demand for a new computer game can…

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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A standard "money demand" function used by macroeconomists has the form In(m) = Bo + B, In(GDP) + B2R, Where m is the quantity of (real) money, GDP is the value of (real) gross domestic product, and R is the value of the nominal interest rate measured in percent per year. Supposed that B, = 2.15 and B, = -0.06. %3D What is the expected change in m if GDP increases by 3%? The value of m is expected to V by approximately%. (Round your response to the nearest integer) What is the expected change in m if the interest rate increases from 1% to 9%? The value of m is expected to ▼ by approximately %. (Round your response to the nearest integer)
Suppose that the dollar cost of producing x appliances is c(x) = 700 + 110x -0.4x² a. Find the average cost per appliance of producing the first 130 appliances. b. Find the marginal cost when 130 appliances are produced. c. Show that the marginal cost when 130 appliances are produced is approximately the cost of producing one more appliance after the first 130 have been made, by calculating the latter cost directly.
2. Consider the function y(x) = 5x over the interval [0, 10]. (a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve represented by the above function, find the slope of the lines (secants) AB, and AC, respectively. (b) If x represents time and y represents the displacement of a particle moving along a line, what is the physical meaning of your results to part (a)? (c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the given function, find the slope of the line DC. (d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?
The U.S. Energy Information Administration projected that imports of petroleum products in 2005 would be 4.81 quadrillion Btu and would increase by 5.47% each year through 2020.T (a) Find the function of the model that gives projected petroleum imports in quadrillion Btu, where t is the number of years since 2005, with data from 0 sts 15 P(t) = quadrillion Btu (b) According to the model, when will imports exceed 7 quadrillion Btu? (Round your answer for t to two decimal places.) Imports will exceed 7 quadrillion Btu in t= years which will occur in the year (c) Describe the end behavior of the model as time increases. P(t) increases without bound as t increases. O P(t) approaches a limiting value of 33.67 as t increases. OP(t) decreases without bound as t increases P(t) remains constant as t increases. OP(t) decreases toward 0 as t increases
Assume that it costs a company approximately C(x) = 400,000 + 120x + 0.002x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.
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).

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