Exam 5: Accumulated Change: the Definite Integral

A local business produces souvenirs for the tourist trade. The business has fixed costs of $6 thousand, and it costs an additional $9.93 thousand in variable costs to produce 10 thousand souvenirs. A consultant told the business that their marginal cost function is dollars per thousand souvenirs. What will it cost to increase their production to 19 thousand souvenirs?

The marginal cost function for a manufacturing company is given by dollars per box, where q is the number of boxes manufactured. If , find the total cost of manufacturing 10 boxes. Round to the nearest dollar.

If the velocity function is measured in feet per second and t gives time in seconds, what are the units of measurement for ?

The Ethnic food line at the Cougar Eat can serve customers at the rate of about 30 per hour. From 10 am until 4 pm one day, the rate R at which customers entered then line was about customers per hour at t hours past 10 am. About when was the waiting line the longest?

At time t, in seconds, the velocity v, in miles per hour, of a car is given by for . Use to estimate how many miles were traveled during this time (average left- and right-hand sums).

The balance in an investment account increases at a rate of dollars per year, where t is time in years since 2000. Make a table of values for R and use it to give a n upper estimate for the total change in the value of the account between 2000 and 2004.

Use the following table to estimate the area between and the x-axis on the interval .

Estimate the area of the region under the curve for . Round to 2 decimal places.

Use the following table to estimate using .

If , , and , find the value of .

A water line made of PVC decays and eventually breaks. The rate that water flows into the street from the break is given by the function , in gallons per hour. Use a calculator or graph to determine how many gallons of water have been lost from the water line break after 13 hours.

Suppose and . Then has a local _______ (maximum/minimum) on at x = _____.

The graph of f is shown in the following figure. Find if and .