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)
- The following table shows total military and arms trade expenditure for a certain country in 2000, 2006, and 2012. Year t (year since 2000) 0 6 12 Military Expenditure C(t)($ billion) 380 540 660 (a) Compute the average rate of change of C(t) over the period 2006–2012 (that is, [6, 12]). Be sure to state the units of measurement. Interpret the average rate of change. This country's military expenditure increased at an average rate of about between 2006 and 2012. (b) Compute the average rate of change of C(t) over the period [0, 12]. Be sure to state the units of measurement. (Round your answer to two decimal places.) Interpret the average rate of change. This country's military expenditure increased at an average rate of about between 2000 and 2012.arrow_forwardThe 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_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_forwardDetermine the average rate of change on the given internal function f(x)=x3-2 a.[-1,0] b.[1,2]arrow_forwardmodel a population p if its rate of growth is proportional to the amount present at time tarrow_forward
- A demand function is modeled by x = a / pm where a is a constant and m > 1.Show that ? = −m. In other words, show that a 1% increase in price results in an m% decrease in the quantity demanded.arrow_forwardThe following table shows daily offshore crude oil production by a country's national oil company, for 2008–2013.Year t (year since 2008) 0 1 2 3 4 5Daily OffshoreProduction s(t) (million barrels) 2.45 2.32 2.19 2.10 2.10 2.10(a) Use the data in the table to compute the average rate of change of s(t) over the period 2008–2013. million barrels/year Interpret the result.During 2008–2013, daily imports from the country were increasing.During 2008–2013, daily imports from the country were decreasing. During 2008–2013, daily imports from the country were constant. (b) Which of the following is true?From 2008 to 2013, the two-year average rate of change of offshore crude oil production for the country increased in value.From 2008 to 2013, the two-year average rate of change of offshore crude oil production for the country decreased in value. From 2008 to 2013, the two-year average rate of change of offshore crude oil production for the country…arrow_forwardSec 2.1: #41. Find the net change in the value of the function between the given inputs.arrow_forward
- The 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_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_forwardUse the following table to answer the question: x -25 -13 -3 0 9 11 h(x) 6 0 -5 -7 -14 -30 What is the average rate of change of h(x) over the interval -13 < x < 11?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