In Exercises 9–12 the function gives the cost to manufacture x items. Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated and
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Finite Mathematics and Applied Calculus (MindTap Course List)
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardWorld Military Expenditure The following chart shows total military and arms trade expenditure from 2011–2020 (t = 1 represents 2011). †A bar graph titled "World military expenditure" has a horizontal t-axis labeled "Year since 2010" and a vertical axis labeled "$ (billions)". The bar graph has 10 bars. Each bar is associated with a label and an approximate value as listed below. 1: 1,800 billion dollars 2: 1,775 billion dollars 3: 1,750 billion dollars 4: 1,730 billion dollars 5: 1,760 billion dollars 6: 1,760 billion dollars 7: 1,850 billion dollars 8: 1,900 billion dollars 9: 1,950 billion dollars 10: 1,980 billion dollars (a) If you want to model the expenditure figures with a function of the form f(t) = at2 + bt + c, would you expect the coefficient a to be positive or negative? Why? HINT [See "Features of a Parabola" in this section.] We would expect the coefficient to be positive because the curve is concave up. We would expect the coefficient to be negative because the…arrow_forwardCell Phones Using the CTIA Wireless Survey for1985–2009, the number of U.S. cell phone subscribers (in millions) can be modeled byy = 0.632x2 - 2.651x + 1.209where x is the number of years after 1985.a. Graphically find when the number of U.S.subscribers was 301,617,000.b. When does the model estimate that the number ofU.S. subscribers would reach 359,515,000?c. What does the answer to (b) tell about this model?arrow_forward
- Sec 2.4: #19. A function is given. Determine (a) the net change and (b) the average rate of change between the given values of the variable.arrow_forwardSuppose that the demand x (in units) for a product is x = 5,000 – 50p, where p dollars is the market price per unit. Then the consumer expenditure for the product is E = px = 5,000p – 50p². For what market price will expenditure be greatest? $arrow_forwardSuppose that the demand x (in units) for a product is x = 15,000 - 150p, where p dollars is the market price per unit. Then the consumer expenditure for the product is E = px = 15,000p – 150p². For what market price will expenditure be greatest? $arrow_forward
- 3. A rocket weighs 2000 tons at liftoff and burns fuel at a rate of 10 tons/minute. Express the rocket's weight W(in tons) as a function of the time t (in minutes) after liftoff.arrow_forwardChoose whether the following statement is true or false. Average rate of change of a function between x = a and x = b can never be greater than the instantaneous rate of change between the same x values. True Falsearrow_forwardUse this information to solve Exercises 9–11:A company is planning to produce and sell a new line of computers. The fixed cost will be $360,000 and it will cost $850 to produce each computer. Each computer will be sold for $1150. 9. Write the cost function, C, of producing x computers. 10. Write the revenue function, R, from the sale of x computers. 11. Determine the break-even point. Describe what this means.arrow_forward
- "For Chapter 12 Data Set 2, compute the t value manually and write a conclusion as to whether there was a change in tons of paper used as a function of the recycling program in 25 different districts. (Hint: Before and after become the two levels of treatment.) Test the hypothesis at the .01 level."arrow_forwardSuppose the production level is 982 car seats. Compute the instantaneous rate of change of revenue at this production level. Is the revenue 1. increasing or 2. decreasing? Enter 1 or 2.arrow_forwardMy work has been attached and the chart. Need to understand side parts D and E. D) Compare the predicted change in greenhouse gas emissions between 2020 and 2025 to the change between 2025 and 2030? During which five-year period is the predicted change greater and by how much or is it the same in the two time periods? E) During what year does this function rule predict that the US emission of greenhouse gasses will decrease to 1000 million metric tons of carbon dioxide equivalents?arrow_forward
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