Week+23+Feb+16-20

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Monday Feb 16
President's Day Holiday

Tuesday Feb 17
Continuing our study of the Average Value of a function, we did a worksheet of problems which are shown below. Solutions, courtesy of the stuents, should appear shortly.

1. A metropolitan newspaper currently has a daily circulation of 50,000 newspapers. The management of the paper decides to initiate an aggressive advertising campaign to increase circulation. Suppose that the daily circulation (in thousands of papers) t days after beginning the campaign is given by

a) What is the average daily circulation during the first 30 days of the campaign?

b) What is the average daily circulation during the next 30 days of the campaign?

2. Suppose cash reserves (in thousands of dollars) are approximated by C(x) = 1 + 12x - x² where x is the number of months after the first of the year. What is the average cash reserve for the first quarter?

3. The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. a) Find the average cost per unit if 1,000 dictionaries are produced?

b) Find the average value of the cost function over the interval [0,1000].

4. A drug is injected into the bloodstream of a patient through her right arm. The concentration of the drug in the bloodstream of the left arm t hours after the injection is given by

a) What is the average concentration of the drug in the bloodstream of the left arm during the first hour after the injection?

b) During the first two hours after the injection, would you expect that the average concentration would be higher or lower than your answer to (a)? Find it!

5. Suppose that the total cost (in thousands of dollars) for manufacturing x sailboats per year is given by C(x) = 575 = 25x - x²/4. for values of x in [0,50]. Find the average rate of change in the total cost of manufacturing the first 30 sailboats.

6. Suppose a wholesaler receives a shipment of 1200 cases of boxes of chocolates every 30 days. The chocolates are sold to retailers at a steady rate and, x days after the shipment arrives, the inventory of cases still on hand is I(x) = 1200 - 40x. If the cost of holding one case is 3 cents per day, find the average daily holding cost.

Wednesday Feb 16
Fundamental Theorem Part 2 Investigation and practice.See slide show. media type="custom" key="3178412"

Thursday Feb 17
Today we built on our understanding between the definite integral and the area under a curve.The following graphics show the problems we did to explore this topic.



Following these examples, we moved on to a worksheet on which we worked for homework and during class on