Worksheet 3 Math 111, Gedeon, Fall 15

Transcription

1 Worksheet 3 Math 111, Gedeon, Fall Consider the graph of the function Q = f(x) given below. 4 y x (a) On which interval(s) is Q increasing? (b) On which interval(s) is Q decreasing? (c) Find the average rate of change of Q on the interval [ 1, 1]. 1

2 2. Let H(t) = 4 t 1. (a) Find the average rate of change in H on the interval [ 2, 0]. (b) Find the percentage rate of change in H on the interval [ 2, 0]. 3. Crude oil production by OPEC during the years 2000 to 2011 roughly followed the supply function S(p) = 0.003p p million barrels produced each day at a price of p dollars per barrel. (a) Find the average rate of change in S on the interval [1, 3]. (b) Interpret your answer to part (a). 2

3 4. Identify whether or not the following points are collinear; (0, 1), (2, 5), (10, 15). 5. Construct a linear model for f(t) from the information given: (a) The graph of f(t) contains the point ( 1, 2) and the function has slope equal to 3. (b) The function s graph contains the points (2, 3) and (4, 6). 3

4 6. Mike Wazowski is going to enroll in Monsters University but must take out student loans. Tuition is $50 per credit taken plus an enrollment fee of $300 per semester. (a) Write a formula that gives the total cost of tuition per semester, T (c), if Mike takes c credits. (b) How many credits did Mike take if his total tuition for the semester is $850? (c) Mike can take out a maximum of $3,200 in student loans. If he takes an average of 10 credits per semester, how many semesters will his loans cover? (d) Suppose Mike gets a part-time job in the school library. The school gives him a $300 deduction on his enrollment each semester in lieu of payment. Give a new formula, D(c), that gives Mike s total cost of tuition if Mike takes c credits. (e) Find c so that D(c) = 3200 and interpret your result. 4

5 7. In order to be a functioning human being, I need to drink Red Bull. At the EMU, I can buy Red Bull for $2.25 per can. The Duck Store sells one can of Red Bull for $2.00. However, each time I go to the Duck Store, I also buy a breakfast burrito for $3.00. (a) Write the total cost of my purchase if I buy x cans of Red Bull and one breakfast burrito at the Duck Store. (b) Write the total cost of my purchase if I buy x cans of Red Bull at the EMU. (c) Find the intersection of the two functions and interpret it in terms of the problem. (d) If I m going to buy 5 cans of Red Bull would my total purchase be more if I went to the Duck Store or the EMU? What about if I buy 15 cans of Red Bull? Hint: Use your answer from part (c). 5

6 8. George Bluth owns a frozen banana stand. The profit, in dollars, of selling b frozen bananas is given by P (b) = 1.5b 300. (a) Interpret the slope and intercept in terms of the situation. (b) How many frozen bananas must George sell in order to break even? 9. Two of my officemates are having a cookie eating contest. Travis eats 10 cookies per minute. Bibby can only eat 7 cookies per minute. To make the contest fair, Bibby is given an automatic bonus of 5 cookies (that is, at time t = 0, Bibby has already eaten 5 cookies). (a) Give the linear function T (t), the number of cookies Travis has eaten after t minutes of the contest. (b) Give the linear function B(t), the number of cookies Bibby has eaten after t minutes of the contest. (c) How many cookies must Travis eat during the contest in order to win? 6