Concept explainers
Marginal Analysis In Exercises 13–18, use
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Chapter 3 Solutions
CALCULUS: APPLIED APPROACH LOW COST MA
- . Marriage Rate The marriage rate per 1000 unmarriedwomen for the years 1987–2014 can be modeled bythe function 132x + 1000y = 9570, where x is thenumber of years after 1980. During what year doesthe equation indicate the marriage rate will be 4.29?(Source: National Vital Statistics Report 2010)arrow_forwardIn Exercises 7–12, describe the relationship between the two quantities.arrow_forwardAt a peach packaging plant, 46,000 lbs of fresh peaches are processed and packed each hour. The table shows the diminishing inventory of peaches over the hour. Remaining peaches are sent to another part of the facility for canning. Peach Inventory Time, t(hours) Peaches, P(thousand pounds) 0 46 0.25 38 0.50 35 0.75 33 1.00 26 .(b) Use the model (not the table of data) to estimate how many peaches are left in inventory after half an hour. (c) Use the model (not the table of data) to estimate how many peaches will be sent to canning.arrow_forward
- The following table shows net income I Of and art dealer when he pays for supplies and sells n items. Find a linear model for the net income as a function of numbers of items sold. arrow_forwardThe profit earned by selling soap at a craft show can be modeled by the graph of the linear function shown on the grid below. What is the rate of change of the profit earned with respect to the number of bars of soap sold?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
- Which of the following shows that the price p increases as the demand d increases?arrow_forwardThe water level in a glass decreases 0.4 cm each hour due to evaporation. At the beginning of the experiment, the water level is 12.6 cm. Let x represent time, in hours, elapsed since the beginning of the experiment and let y represent the water level, in centimeters. Part A Construct a linear function, using x and y from above, that determines the water level at a given time, in hours, after the experiment begins. Part B How many hours does it take for all of the water to evaporate? ____ hoursarrow_forwardThe federal tax code allows some items used for business purposes to be depreciated. That is, their taxable value decreases over time. A new van used in your delivery business has a taxable value of $27,000. The tax code allows you to depreciate this van by$2100 per year. Find a linear function that gives the taxable value T, in dollars, of the van after n years of depreciation.arrow_forward
- #35 please explain wellarrow_forwardRetail Sales November and December retail sales,excluding autos, for the years 2001–2010 can be modeled by the function S(x) = -1.751x2 + 38.167x +388.997 billion dollars, where x is the number ofyears after 2000.a. Graph the function for values of x representing2001–2010.b. During what years does the model estimate thesales to be $550 billion?c. The recession in 2008 caused retail sales to drop.Does the model agree with the facts; that is, doesit indicate that a maximum occurred in 2008?arrow_forwardLet ŷ represent the profit (in thousands of dollars) for a certain company xx years after 1975. A statistician calculates a linear model ŷ = 1.86xx + 13 Use the model to estimate the profit in 1982. Your answer should be in dollars, not thousands of dollars.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage