Concept explainers
Use Table 1 to evaluate all
92. Politics. The number of voters (in thousands) in a metropoli- tan area is given approximately by
where t is time in years. Find the average number of voters during the period from t = 0 to t = 10.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
- In Problems 49–56, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values.arrow_forwardIn Problems 94–97, the graphs of the given pairs of functions intersectinfinitely many times. In each problem, find four of these points ofintersection.arrow_forwardIn Problems 13–24, use the graph of the function f given.arrow_forward
- In the section opener, we saw that 80x – 8000 f(x) 30 s xs 100 110 models the government tax revenue, f(x), in tens of billions of dollars, as a function of the tax rate percentage, x. Use this function to solve Exercises 55–58. Round to the nearest ten billion dollars. 55. Find and interpret f(30). Identify the solution as a point on the graph of the function in Figure 6.4 on page 439. 56. Find and interpret f(70). Identify the solution as a point on the graph of the function in Figure 6.4 on page 439. 57. Rewrite the function by using long division to perform (80x - 8000) - (x - 110). Then use this new form of the function to find f(30). Do you obtain the same answer as you did in Exercise 55? Which form of the function do you find easier to use? 58. Rewrite the function by using long division to perform (80x – 8000) - (x – 110).arrow_forward2) The Nikkei 225 index is a stock market index for the Tokyo Stock Exchange. The Nikkei 225 index for the period 1990-2010 can be modeled by V (t) = 23,500e-0.0381t where t is the number of years after 1990. Determine how many years after 1990 the Nikkei 225 index reached $20,000.arrow_forwardb. Are there any critical values for either graph? Where are the intersections between the two? What do these intersections represent? c. Find the points where the hours of daylight are at a maximum/minimum. Around what time of the year are these points? Compare the information. d. What tools did you use to solve this problem? What other ways could you have come to find the same solution? e. How many hours of daylight are in each location at t=5? at t=8?arrow_forward
- 11–24, find the constant of variation for each of the stated conditions. y varies inversely as x, and y= -4 when x= 1/2 . Kaufmann, Jerome E.; Schwitters, Karen L.. Intermediate Algebra (p. 487). Cengage Learning. Kindle Edition.arrow_forwardIn Problems 11–18, match each graph to its function. A. Constant function E. Square root function B. Identity function F. Reciprocal function C. Square function G. Absolute value function D. Cube function H. Cube root function 11. 12. 13. 14. 15. 16. 17. 18.arrow_forwardIn Problems 6–11, find the domain of each functionarrow_forward
- Suppose that 40 deer are introduced in a protected area. The population of the herd P can be modeled by P = 40 + 20x / 1 + .05x where x is the time in years since introducing the deer. Determine the time required for the deer population to reach 200.arrow_forwardIn Problems 31–42:(a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function.(d) Based on the graph, find the range. (e) Is f continuous on its domain?arrow_forwardPoint A is launched horizontally away from a wall and a(t) represents Point A's distance from the wall (in meters) in terms of the number of seconds t since the point was launched. Point B is also launched from the wall, but travels 2.5 times as fast as Point A. A Click here to launch the points. a. Suppose b(t) represents Point B's distance from the wall (in meters) in terms of the number of secondst since the points were launched. Write a function formula for b using the function a. b(t) = Preview b. The graph of function a is shown below (in black). Sketch the graph of function b. 20 16 12 8. 4 1 3 4 5 Clear All Draw:arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education