Exam 13: Indefinite Integrals

The DeWitt Company has found that the rate of change of its average cost of producing a product is , where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00. Find the average cost of producing 140 units of the product. Round to the nearest dollar. ​

Evaluate the integral . ​

Suppose the rate of change of the interest paid on the public debt of the United States as a percent of federal expenditures can be modeled by , where t is the number of years past 1930. Use integration and the fact that in 1975, the interest paid as a percent of Federal Expenditures was 12.7, to find the function D(t) that models the interest paid on the public debt of the United States as a percent of federal expenditures. If it's necessary, round your calculations to three decimal places. ​

Write the indefinite integral that gives the family associated with . ​

The rate of production of a new line of products is given by , where x is the number of items and t is the number of weeks the product has been in production. Assuming that when , find out the number of items produced in the fifth week. Round your answer to the nearest whole number. ​

If $P is invested for n years at 51% compounded continuously, the rate at which the future value is growing is . What function describes the future value at the end of n years? Round your answer to two decimal places, if necessary. ​

Evaluate the integral . If it's necessary, round your calculations to one decimal place. ​

Find a function g(x) such that . ​

Evaluate the integral . ​

Evaluate the integral . ​

A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family. ​ ​ ​

Suppose that the marginal revenue for a certain product is given by , where x is in thousand of units and revenue is in thousands of dollars. Find . Round your calculations to two decimal places, if necessary. ​

Evaluate the integral . ​

Suppose that in a certain, company, the relationship between the price per unit p of its product and the weekly sales volume y, in thousands of dollars, is given by . Solve this differential equation if when . ​

Evaluate the integral . ​

Because a new employee must learn an assigned task, the employee's production will increase with time. Suppose that for the average new employee, the rate of performance is given by , where N is the number of units completed t hours after beginning a new task. If 3 units are completed after 8 hours, how many units are completed after 80 hours? ​

The average cost of a product changes at the rate and the average cost of 12 units is $18.00. Find the average cost function . ​

Find the particular solution to the given differential equation. ​ when ​

A certain firm's marginal cost for a product is , its marginal revenue is , and its total cost of production of 11 units is $1,243. Find the profit function P.

Suppose that the marginal revenue (in dollars) from the sale of x units of a product is . What is the revenue from the sale of 170 units of the product? Round your answer to the nearest cent. ​