11) A consumer's level of utility from consuming a certain good s is given by thefollowing function:U(x) = 1.5x² - 12Due to a shift in the consumer's taste and preferences they will now derive 2 moreunits of utility for consuming the same amount of good x as before.(a)Sketch the original utility function of good .x.(b) Why is it necessary that x > 0?(c) Determine the new utility function of this company.(d) Using your graph in (i) sketch the transformed utility function.for x > 0

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Answered: 11) A consumer's level of utility from…

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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2. Lijah opened an account at Advantis Credit Union. The balance of her account after x years is represented by the function b(x) = 500(1.05)*. What annual interest rate is Lijah earning? а. b. After how many years did it take for Lijah's balance to double? Show all of your work.
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.
3. You and your roommate, a mechanical engineer, each modelled the heat transfer of an industrial process unit and obtained the following two different expressions for the temperature (°C) of the unit as a function of time (min). You: T (t) = 100 (1- exp (-0.2t)) Roommate T (t) = 40 exp (-0.01t) At what time would the temperature be the same for the two of you and what would the temperature be at that time?
1. A liquid starts at an initial temperature of 175 C and cools down in a room held at a constant temperature of 16 C. It's temperature can be modeled, as a function of time cooling, by the equation y=a(b) +c. which of the following statements is true? (1) a=159 andc=16 (3) a=175 andc=16 (2) a=16 andc=159 (4) a=16 and c=175 14
c) A university projects that enrollments are going to decline as the pool of college-aged applicants begins to shrink. They have estimated the number of applications for coming years to behave according to the functiona = f(t) = 6,500 – 250twhere a equals the number of applications for admission to the university and t equals time in years measured from this current year (t = 0).i. What class of function is this?ii. What is the expected number of applications 5 years from today? 10 years?iii. Do you think this function is accurate as a predictor indefinitely into the future? iv. What kinds of factor would influence the restricted domain on t?
1. Suppose the function C(r) represents the cost to produce rope as a function of the length of the rope. (a) What can you conclude about C from the statement "The cost of production is increasing at a decreasing rate"? Pick one of positive, negative, zero, or other. If other, please explain. i. C"(r) is ii. C"(r) is (b) What can you conclude about C from the statement "The cost of production is decreasing at an increasing rate"? Pick one of positive, negative, zero, or other. If other, please explain. i. C"(r) is ii. C"(r) is
11. The profit, P, in dollars, of a company is a function of the number of tons of cement, C, it has produced and is given by: P(C) = 2000C – C² -1000 a. At what rate, with respect to the number of tons of cement produced, is the profit changing when 500 tons have been produced? b. The number of tons of cement produced is changing at a rate of 100 tons/minute. At what rate, with respect to time, is the profit changing when 500 tons have been produced?
b) y=-4/T O Increasing function O Decreasing function Neither increasing nor decreasing function
1. Consider the following function: f (x) = 3x – 2x2 a. Find the derivative function f'(x) using the limit definition of the derivative. b. Use the derivative function to evaluate f'(-1) and f'(2) Given the graph of a function f(x), which is shown to the right, sketch the graph of its derivative f'(x), on the same xy-plane. *Assume the scales of the x-axis and the y-axis are equal.* 2.

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