Exam 12: Indefinite Integrals

Suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by , where t is the number of years past 1960. The value of are approximately $19,312.13 and $1,162.81 respectively which are been evaluated by using the arbitrary constant that is been evaluated by using the data point from 1960. Interpret . Round your answer to two decimal places, if necessary. ​

Evaluate the integral . ​

If consumption is $6.3 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 calculations to three decimal places. ​

The marginal revenue for a new calculator is given by , where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators. ​

Use integration to find the general solution to the differential equation . ​

Evaluate the integral . ​

Suppose that the marginal revenue for a product is and the marginal cost is with a fixed cost of $900. How many units will result in a maximum profit? ​

Suppose that the marginal cost (in dollars) for a product is and its fixed cost is $380.00. If the marginal revenue (in dollars) for the product is , find the profit or loss from production and sale of 35 units. ​

Suppose that the marginal propensity to save is (in billions of dollars), and that consumption is $7.50 billion when disposable income is 0. Find the national consumption function. Round your answer to two decimal places. ​

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

Evaluate the integral . ​

Evaluate the integral . ​

Suppose that the marginal revenue for a product is and the marginal cost is , with a fixed cost of . Find the profit or loss from the production and sale of 3 units. ​

Evaluate the integral . ​

Evaluate the integral . ​

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. ​

The impact of inflation on a fixed pension can be severe. If P represents the purchasing power (in dollars) of a $40,000 pension, then the effect of a 2% inflation rate can be modeled by the differential equation , where t is in years. Find the purchasing power of the pension after 35 years. Round to the nearest dollar. ​

Evaluate the integral . ​

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. ​