Calculus (414 problems)

Evaluate .

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

A bicycle producing factory was founded in 1985. The number of bicycles produced t years thereafter is given by:

.

For what year between 1987 [t=2] and 1995 [t=10] (both years included) was the production of bicycles the largest, and for what year was the production the smallest? How many bicycles were produced in each of these years?

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?

After x weeks the number of persons using a new drug was .

(a) At what percentage rate was the use of the drug changing after four weeks?

(b) By how much did the number of persons using this drug actually change during the fourth week?

Determine the differentialif

Assume that the population in year 2008 is given by

where t is measured in years after 2008.

(a) Compute the current population

(b) Compute the population in year 2033

(c) What happens with the population when t is very large.

Express the distance between the point (3, 0) and the point P (x, y) of the parabola y = x² as a function of x.

Use tabular integration to compute

A manufacturer estimates marginal revenue to be dollars per unit when the level of production is q units. The corresponding marginal cost has been found to be 0.4q dollars per unit. Suppose the manufacturer’s profits is $520 when the level of production is 16 units. What is the manufacturer’s profit when the level of production is 25 units?

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?

Suppose the demand equation for all-day passes to an amusement park is given by
p = 70 – 0.02q, where p is the price of the pass in dollars and q is the number of people attending at that price.

a. What price corresponds with an attendance of 3000 and what is the total revenue at that price?

b. Write the revenue function as a function of attendance and then determine the attendance that will maximize the revenue.

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

A disgruntled employee determines that the company’s profit of the production of x hundred units is dollars. He plans to “get even with the company” by suggesting that it produces the number of items that he knows will minimize their profit. How many units he recommend to the company to purchase?

Money is deposited in a bank offering interest at an annual rate of 6% compounded continuously. Find the percentage rate of change