Integration (125 problems)

The function is a probability distribution

Compute.

For consumers’ demand function

and.

(a) Find the total amount of money consumers are willing to spend to getunits of the commodity.

(b) Sketch the demand curve and interpret the consumer’s willingness to spend as an area

Use tabular integration to compute

Suppose that when it isyears old a particular industrial machine generates revenue at the ratedollars per year, and that operating and servicing costs accumulate a the rate ofdollars per year

(a) How many years pass before the profitability of the machine begins to decline?

(b) What are the net earnings?

(c) Show a graph

The management of a national pizza chain is selling a 6 year franchise to operate its newest outlet. Experience in similar localities suggests thatyears from now the franchise will be generating profit at the rate ofdollars per year. The prevailing rate of interest remains fixed during the next 6 years at 6% compounded continuously. What is the present value of the franchise?

Records indicate thatmonths after the beginning of the year, the price of ground beef in local supermarkets was

dollars per pound. What was the average price of ground beef during the first 3 months of the year?

Use tabular integration to compute

Find the Gini index for the given Lorentz curve

A study indicates thatmonths from now the population of a certain town will be increasing at the rate ofpeople per month. By how much will the population of the town increase over the next 8 months?

Use tabular integration to compute

he administrators of a town estimate that the fraction of people who still be residing in the townyears after they arrive is given by the function

If the current population is 20,000 people and new townspeople arrive at the rate of 500 per year, what will the population be 10 years from now?

Compute the average of the functionover the interval [1, 5].

Money is transferred continuously into an account at the constant rate of $1000 per year. The account earns interest at the annual rate of 10% compounded continuously. How much will be in the account at the end of ten years?

Find the average value of the below function over the specified interval. Sketch the graph of the function along with the rectangle whose base is the given interval and whose height is the average value of the function

Suppose that t years from now, one investment plan will be generating profit at the rate of hundred dollars per year, while a second investment will be generating profit at the rate of

hundred dollars per year.

a) For how many years does the rate of profitability of the second investment exceed that of the first?

b) Compute the net excess profit assuming that you invest in the second plan for the time period determined in part (a)

Sketch the rate of profitability curves and and shade the region whose area represents the net excess profit computed in part (b)

Use tabular integration to compute

The population densitymiles from the center of certain city is

people per square mile. How many people live between 1 and two miles from the city center?

Suppose that a tank initially contains 2000 gal of water and the rate of change of its volume after the tank drains for t min is (in gallons per minute). How much water does the tank contain after it has been draining for 25 minutes?