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 lev
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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_forwardRound off to one decimal place where applicable The table time (xi) 1 2 3 4 5 6infections (yi = f(xi)) 32 37 34 48 53 69 depicts the number of newly infected individuals with a contagious, airborne disease atintervals of 1 day over a period of 6 days. Here i = 0, 1, 2, . . . , 5 and the quantities x0 = 1and y0 = 32, respectively, represent the end of the first day of testing for the disease, andnumber of positive tests conducted by the end of that day.(Note: xi represents the end of a testing day, where the values of xi are as tabulated, whileyi represents the number of positive tests conducted by the end of day xi.) (b) (i) Use the table presented in (a), along with Newton’s forward difference formula, toapproximate f(7) with a polynomial of degree 3, P3(x). Start with x0 = 1. (ii) Estimate the error in the approximation in (b)(i).arrow_forwardThe following table shows the rate R of vehicular involvement in traffic accidents (per 100,000,000 vehicle-miles) as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s Accident rate R 20 1500 25 650 30 350 35 300 40 700 45 1300 c) At what speed is vehicular involvement in traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Round your answer to the nearest whole number.) mpharrow_forward
- The following table shows education expenditure in the United States as a percentage of total federal spending in 2009, 2015, and 2019. (a) Compute and interpret the average rate of change of P(t) over the period of 2009-2019 (that is, [9,19]) and over the period [9,19]. (b) Compute the average rate of change over the period [15,19]arrow_forwardIn Exercises 52-55, refer to Figure 26. Estimate the average rate of change from A to B and from A to C.arrow_forwardProve that the straight line y=3-2x intersects the exponential curve y=e^x at a point whose x-coordinate belongs to the interval (0,1).arrow_forward
- When predicting population growth, demographers must consider birth and death rates as well as the net change caused by the difference between the rates of immigration and emigration. Let P be the population at time t and let N be the net increase per unit time resulting from the difference between immigration and emigration. So, the rate of growth of the population is given byarrow_forwardThe analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?arrow_forward24) Find the maximum rate of change of at the given point and the direction in which it occurs.arrow_forward
- Suppose that the price p of a product and its demand x are related through the price-demand equation 40p+x=5,000. What is the region for which the demand function is elastic? Select the correct answer below: 62.5<p<125. p>62.5 0<p<62.5 p>125.arrow_forwarda) Determine the AVERAGE rate of change of y over each interval −5 ≤ x ≤ 9 −1 ≤ x ≤ 5 −3 ≤ x ≤ 7 b) Based on your answers above, what can you say about the type of function that y represents? c)Estimate the INSTANTANEOUS rate of y at the point x = −3.arrow_forwardAssume that in a certain country, the rate at which jobs are created is proportional to the number of people who already have jobs. If there are 15 million jobs at t = 0 and 15.1 million jobs 3 months later, how many jobs will there be after 2 years?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning