Concept explainers
Sketching graphs of functions Sketch the graph of a function with the given properties. You do not need to find a formula for the function.
29. g(1) = 0, g(2) = 1, g(3) = −2,
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Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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- Population Growth The projected population of the United States for the years 2025 through 2055 can be modeled by P=307.58e0.0052t, where P is the population (in millions) and t is the time (in years), with t=25 corresponding to 2025. (a) Use a graphing utility to graph the function for the years 2025 through 2055. (b) Use the table feature of the graphing utility to create a table of values for the same time period as in part (a). (c) According to the model, during what year will the population of the United States exceed 430 million?arrow_forwardResale Value: The resale value V, in dollars, of a certain car is a function of the number of year t since the year 2012. In the year 2012, the resale ale is 18,000 and each year thereafter the resale value decreases by 1700. a. What is the resale value in the year 2013? b. Find a formula for V as a function of t. c. Make a graph of V versus t covering the first 4 years since the year 2012. d. Use functional notation to express the resale value in the year 2015, and then calculate that value.arrow_forwardSwimming Laps Miyuki practices swimming laps with her team. The function y=f(t) graphed below gives her distance in meters from the starting edge of the pool t seconds after she starts her laps. Describe in words Miyukis swim practice. What is her average speed for the first 30 s? Graph the function y=1.2f(t). How is the graph of the new function related to the graph of the original function? What is Miyukis new average speed for the first 30 s?arrow_forward
- Arboriculture The growth of a red oak tree is approximated by the function G=0.003t3+0.137t2+0.458t0.839,2t34 where G is the height of the tree (in feet) and t is its age (in years). (a) Use a graphing utility to graph the function. (b) Estimate the age of the tree when it is growing most rapidly. This point is called the point of diminishing returns because the increase in size will be less with each additional year. (c) Using calculus, the point of diminishing returns can be found by finding the vertex of the parabola y=0.009t2+0.274t+0.458. Find the vertex of this parabola. (d) Compare your results from parts (b) and (c).arrow_forwardField Trip A class of fourth graders walks to a park on a field trip. The function y=f(t) graphed below gives their distance from school in ft t minutes after they left school. What is the average speed going to the park? How long was the class at the park? How far away is the park? Graph the function y=0.5f(t). How is the graph of the new function related to the graph of the original function? What is the average speed going to the new park? How far is the new park? Graph the function y=f(t10). How is the graph of the new function related to the graph of the original function? How does the field trip described by this function differ from the original trip?arrow_forwardFormulas The volume V of a rectangular box is determined by the length, the width, and the height. For a particular set of boxes, the height is 4 feet, the length is given as x feet, and the width is 3x feet. Express the volume as a function of x.arrow_forward
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