Petrochemical Production p (Billions of metric tons)

Transcription

1 Off-Line Homework Section 1.1 WebAssign Section 1.1 #13 (ebook 1.1#42) The following table shows the annual petrochemical production p in Mexico by Pemex, Mexico s national oil company, for (t = 0 represents 2005). Year t (Years since 2005) Petrochemical Production p (Billions of metric tons) (a) Find p(0), p(2) and p(4). Interpret your answers. Answer in sentences, and include units. (b) What is the domain of p? Express your answer as an inequality and in interval notation. (c) Represent the data graphically and use your graph to estimate p(2.5). Interpret your answer. Answer in a sentence and include units. Petrochemical Production (billions of metric tons) Time (years since 2005)

2 Off-Line Homework Section 1.1 WebAssign Section 1.1 #14 (ebook 1.1#50) The number of research articles in Physical Review that were written by researchers in the United States from 1983 through 2003 can be approximated by A(t) = 0.01t t hundred articles (t is the time in years since 1983). (a) Find an appropriate domain of A. Express your answer as an inequality and in interval notation. (b) Compute A(10). What does the answer say about the number of research articles? Answer in a sentence, and include units. Similar to WebAssign Section 1.1 #15 and 16 (ebook 1.1#47) The following graph shows the approximate annual after-tax net income P(t), in millions of dollars of Continental Airlines for (t = 0 represents 2005). 600 Income (millions of dollars) Time (years since 2005) (a) Estimate P(0), P(4), and P(3.5) to the nearest 100 million dollars. Interpret your answers. Answer in a sentence (or sentences), and include units. (b) At which of the following values of t is P(t) increasing most rapidly: 0, 0.5, 1, 2.5, 3.5? Interpret your result in a sentence (refer to a year, like 1980, rather than a value of t).

3 Off-Line Homework Section 1.2 WebAssign Section 1.2 #2 (ebook 1.2#18) The cost of renting tuxes for the Choral Society s formal is $20 down, plus $88 per tux. a. Express the cost C as a function of x, the number of tuxedos rented. Use your function to answer the following questions. Include units. b. What is the cost of renting 2 tuxes? c. What is the cost of renting the 2 nd tux? d. What is the cost of renting the 4,098 th tux? e. What is the variable cost? What is the fixed cost? What is the marginal cost? What are the units on marginal cost? f. Graph C as a function of x. Label the axes (include units) and scale on the graph. Mind the units Say your answer to a question was $1, That s the same as thousand dollars. If the instructions say to round to the nearest dollar, you get dollars, which is the same as thousand dollars. Axis label: Axis label:

4 Off-Line Homework Section 1.2 WebAssign Section 1.2 #4 (ebook 1.2#20) The Audubon Society at Enormous State University (ESU) is planning its annual fund-raising Eat-a-thon. The society will charge students 50 per serving of pasta. The only expenses the society will incur are the cost of the pasta, estimated at 15 per serving, and the $350 cost of renting the facility for the evening. a. Write the associated cost C(x), revenue R(x) and profit P(x) functions. b. How many servings of pasta must the Audubon Society sell in order to break even? (Answer in a sentence, including units with the numbers.) c. What profit (or loss) results from the sale of 1,500 servings of pasta? Include units. WebAssign Section 1.2 #5 (ebook 1.2#21) Gymnast Clothing manufactures expensive hockey jerseys for sale to college bookstores in runs of up to 200. Its cost (in dollars) for a run of x hockey jerseys is C(x) = x + 0.2x 2 (0 x 200) Gymnast Clothing sells the jerseys at $100 each. a. Find the revenue R(x) and profit P(x) functions. b. How many jerseys should Gymnast Clothing manufacture to make a profit? Round your answer to the nearest whole number. Include units.

5 Off-Line Homework Section 1.2 WebAssign 1.2 #9 (ebook 1.2#28) The Metropolitan Company sells its latest product at a unit price of $5. Variable costs are estimated to be 50% of total revenue, while fixed costs amount to $7,600 per month. How many units should the company sell per month in order to break even, assuming hat it can sell up to 5,000 per month at the planned price? Answer in a sentence, including units with the numbers.)

6 Off-Line Homework Section 1.3 WebAssign Section 1.3 #5 (ebook Section 1.3#13) Decide which of the two given functions is linear and find its equation. x f (x) g(x) WebAssign Section 1.3#18 (ebook Section 1.3#82) If it costs Microsoft $1,230 to manufacture 8 Kinects per hour for the Xbox-360 and $2,430 to manufacture 16 per hour at a particular plant, obtain the corresponding linear cost function. a. Write a formula for the cost function. What does each additional Kinect mean? Do part (a) then answer these questions: If you currently manufacture 16 per hour, and you want to manufacture one more per hour, how much more would it cost you to do that? Answer = C( ) C( ) = b. What was the cost to manufacture each additional Kinect? (Read the box. Include units.) Or if you currently manufacture 10 per hour and you want to manufacture 11 per hour, how much more would that cost you? Answer = C( ) C( ) = Did you get the same answer? Yes / No What part of the cost function gives you that formula? c. Use the cost function to estimate the cost of manufacturing 36 Kinects per hour. (Include units.) Fill in the blank: The cost to produce an additional Kinect per hour is the of the cost function. This is also called the cost.

7 Off-Line Homework Section 1.3 WebAssign 1.3#20 (ebook 1.3 #85) The following table shows worldwide sales of cell phones by Nokia and their average wholesale prices in the first quarters of 2009 and Quarter Q Q Wholesale Price (dollars) Sales (millions) a. Use the data to obtain a linear demand function for (Nokia) cell phones. Use p for price and q for sales level. b. Use your demand equation to predict sales if Nokia lowered the price further to $75. Include units (careful!). c. Fill in the blank: For every $1 increase in price, sales of cell phones (circle one) increases / decreases by million cell phones. d. Fill in the blank: In general, when x and y are related by the linear equation y = mx + b, for every 1-unit increase in x, the y-value changes by units. e. Another cell phone company expects to sell q million phones when they set the price at p dollars, where q = 291 3p. Write a sentence like the one in part (c) to interpret the slope in this demand equation.

8 Off-Line Homework Section 1.4 WebAssign Section 1.4#1 and 2 (ebook 1.4#2 and 5) Consider the following data and model. Data (x, y): (0, 1), (1, 1), (2, 2) Model: y = x + 1 x Observed value Predicted value Residual a. Complete the table (vocabulary check). b. Plot the data and graph the model on the axes provided c. What does SSE stand for? Compute the SSE Now consider the same data with another model. Data (x, y): (0, 1), (1, 1), (2, 2) Model: y = x x Observed value Predicted value Residual d. Complete the table. 0 e. Plot the data and graph the model on the axes provided. f. Compute the SSE g. Which model is a better fit? How do you know? Write a sentence

9 Off-Line Homework Section 1.4 WebAssign 1.4 #4-8 Spread sheet tasks a. Referring to the excerpt from a spreadsheet below, write the formula you would use in cells C2, D2, E2 and E10. C2 D2 E2 E10 Why do you include $ in front of F2 and G2 when you use those cells in your formula. (You did, didn t you? They should look like $F$2 and $G$2.) What would happen in the Spreadsheet if you left off the = at the beginning of each formula? (You didn t leave them off, did you?) A B C D E F G 1 Predicted Value Square of Observed y = mt + b Residual x residual m b where m is in F2 and b is in G Fill down to complete this part SSE

10 1 Math 115 Off-Line Homework Section 3.4/3.5/3.6 WebAssign Section 3.4/3.5/3.6 #1 (ebook Section 3.4#26) The following table shows the percentage of the U.S. Discretionary Budget allocated to education in 2003, 2005 and 2009 (t = 0 represents 2000). Compute and interpret the average rate of change of P(t) over the given periods: Year t Percentage P(t) a. The period from 2003 to Answer in a sentence and include units with your answer. b. The period from 2005 to Answer in a sentence and include units with your answer. WebAssign Section 3.4/3.5/3.6 #2 (ebook Section 3.4#10) Calculate the average rate of change of the given function over the given interval. Use correct units with your answer. The y-axis is in dollars. Here a = 20, b = 24, and c = 28. Interval [1, 5]. Average rate of change (include units!):

11 2 Math 115 Off-Line Homework Section 3.4/3.5/3.6 WebAssign Section 3.4/3.5/3.6 #4 (ebook Section 3.4#13) Calculate the average rate of change of the function f (x) = x 3 3 over the interval [1, 3]. WebAssign Section 3.4/3.5/3.6 #6 (ebook Section 3.5#7) Consider the function as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. R(t) = t 3 a. Find the average rate of change of R over the intervals [t, t + h], where t = 1 and h = 1, 0.1, and 0.01 days. Record your answers in the table. The average rate of change of R for t in the h Interval interval [1, 1 + h] units: 1 [1, 2] 0.1 [1, 1.1] 0.01 b. Use your answers to estimate the instantaneous rate of change of R at t = 1. Include units with your answer.

12 3 Math 115 Off-Line Homework Section 3.4/3.5/3.6 Definition The definition of the derivative of a function f (x) is given by WebAssign Section 3.6 #9 (ebook Section 3.6#15) Compute the derivative f (x) of the given function using the definition. f (x) = x WebAssign Section 3.4/3.5/3.6 #11 (ebook Section 3.6#20) Compute the derivative f (x) algebraically, using the definition. f (x) = 2x 2 + x

13 4 Math 115 Off-Line Homework Section 3.4/3.5/3.6 WebAssign Section 3.4/3.5/3.6 #12 (ebook Section 3.6#25) Compute the derivative f (x) algebraically, using the definition. f (x) = 1 x