The demand function for a certain item is p represents the price of an item and Q represents the number of items sold at that price. (a) Evaluate the demand elasticity when p = 3. E(3) = (b) For what value of p is the demand elasticity unitary? p = 0 percent change in quantity Here, "demand elasticity" is the absolute value of for an infinitesimal change in price, so percent change in price Q = 56√32-p². AQ/Q E= lim Ap 0 Ap/p

The demand function for a certain item is p represents the price of an item and Q represents the number of items sold at that price. (a) Evaluate the demand elasticity when p = 3. E(3) = (b) For what value of p is the demand elasticity unitary? p = 0 percent change in quantity Here, "demand elasticity" is the absolute value of for an infinitesimal change in price, so percent change in price Q = 56√32-p². AQ/Q E= lim Ap 0 Ap/p

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

See similar textbooks

Similar questions

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Continued This is a continuation of Exercise 13. As we saw earlier, the stock turnover rate of an item is the number of times that the average inventory of the item needs to be replaced as a result of sales in a given time period. Suppose that a hardware store sells 80 shovels each year. a. Suppose that the hardware store maintains an average inventory of 5 shovels. What is the annual stock turnover rate for the shovels? How is this related to the yearly number of orders to the wholesaler needed to restock inventory? b. What would he the annual stock turnover rate if the store maintained an average inventory of 20 shovels? c. Write a formula expressing the annual stock turnover rate as a function of the average inventory of shovels, identify the function and the variable, and state the units.
Grazing Kangaroos The amount of vegetation eaten in a day by a grazing animal V of food available measured as biomass, in units such as pounds per acre. This relationship is called the functional response. If there is little vegetation available, the daily intake will be small, since the animal will have difficulty finding and eating the food. As the amount of food biomass increases, so does the daily intake. Clearly, though, there is a limit to the amount the animal will eat, regardless of the amount of food available. This maximum amount eaten is the satiation level. a.For the western grey kangaroo of Australia, the functional response is G=2.54.8e0.004V, where G=G(V) is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Draw a graph of G against V. Include vegetation biomass levels up to 2000 pounds per acre. ii. Is the graph you found in part i concave up or concave down? Explain in practical terms what your answer means about how this kangaroo feeds. iii. There is a minimal vegetation biomass level below which the western grey kangaroo will eat nothing. Another way of expressing this is to say that the animal cannot reduce the food biomass below this level. Find this minimal level. iv. Find the satiation level for the western grey kangaroo. b. For the red kangaroo of Australia, the functional response is R=1.91.9e0.033V, Where R is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Add the graph of R against V to the graph of G you drew in part a. ii. A simple measure of the grazing efficiency of an animal involves the minimal vegetation biomass level described above: The lower the minimal level for an animal, the more efficient it is at grazing. Which is more efficient at grazing, the western grey kangaroo or the red kangaroo?
How are the absolute maximum and minimum similar to and different from the local extrema?
aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line between (a,f(a)) and (b,f(b)).
The inverse demand function for a monopoly's product is p= 107- 10. What is the firm's marginal revenue equation? Marginal revenue (MR) is MR =