Exam 12: Indefinite Integrals

If consumption is $2 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars), find the national consumption function. If it's necessary, round your answer to two decimal places. ​

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.

For which of the following differential equations is a solution? ​

Evaluate the integral . ​

Suppose that a liquid carries a drug with concentration 0.03 g/cc into a 200-cc organ at a rate of 5 cc/s and leaves at the same rate. If initially there is 3 g of drug in the organ, find the amount A of drug in the organ as a function of time t. ​If it's necessary, round your calculations to four decimal places.

Use algebra to rewrite the integrand; then integrate and simplify. ​ ​

Evaluate the integral . ​

The total physical output of a number of machines or workers is called physical productivity and is a function of the number of machines or workers. If is the productivity, is the marginal physical productivity. If the marginal physical productivity for bricklayers is , where P is the number of bricks laid per day and x is the number of bricklayers, find the physical productivity of 5 bricklayers. (Note: when .) ​

Find the general solution to the differential equation . ​

Find a function g(x) such that . ​

Suppose that the marginal propensity to consume is (in billions of dollars), and that consumption is $5.33 billion when disposable income is 0. Find the national consumption function. If it's necessary, round your calculations to four decimal places. ​

Suppose that the marginal propensity to save is (in billions of dollars) and that consumption is $9 billion when disposable income is 0. Find the national consumption function C. Round numbers in our answer to two decimal places when appropriate. If it's necessary, round your calculations to two decimal places. ​

Evaluate the integral . ​​

When the interest on an investment is compounded continuously, the investment grows at a rate that is proportional to the amount in the account. If $25,000 is invested (when ) and the amount in the account after 18 years is $46,940.26, find the interest rate on this investment? Round to one decimal place. ​

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. ​

Find the particular solution to the differential equation that satisfies when . ​

A certain radioactive substance has a half-life of 75 hours. Find how long it will take, to the nearest hour, for 75% of the radioactivity to be dissipated if the amount of material x satisfies (t in hours). Round your answer to the nearest hour. ​

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 y=4 when p=$126. ​

If consumption is $2 billion when disposable income is 0, and if the marginal propensity to save is (in billions of dollars), find the national consumption function. If it's necessary, round your calculations to two decimal places. ​

The average cost of a product changes at the rate and the average cost of 16 units is $22.00. Find the average cost function . ​