Concept explainers
Special Rounding Instructions. For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated.
Growth in Length of Haddock A study by Raitt showed that the maximum length that a haddock could be expected to grow is about
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a. Find an exponential model of
b. Let
c. Plot the graph of the experimentally gathered data for the length
d. A fisherman has caught a haddock that measures
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Rare Coins The table below shows the estimated value C, in dollars, of an 1877 Indian Head Cent Philadelphia mint mark in very fine condition t years after 1950. t=time,inyearssince1950 C=value,indollars 0 25 30 400 45 625 54 1750 60 2000 a.Use exponential regression to model C as an exponential function of t. b.According to your exponential model, by what percentage does the value of the 1877 cent increase from year to year?arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Traffic in the Lincoln TunnelCharacteristics of traffic flow include density D, which is the number of cars per mile, and average speed s in milesperhour.Traffic system engineers have investigated several methods for relating density to average speed. One study considered traffic flow in the north tube of the Lincoln Tunnel and fitted an exponential function to observed data. Those data are partially presented in the table below. Speed s Density D 32 34 25 53 20 74 17 88 13 102 a.Make an approximate exponential model of D as a function of s. b.Express, using functional notation, the density of traffic flow when the average speed is 28mileperhour, and then calculate that density. c.If average speed increases by 1mileperhour, what can be said about density?arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places but round all other answers to two decimal places unless otherwise indicated. Grazing Rabbits The amount A of vegetation measured in pounds eaten in a day by a grazing animal is a function of the amount V of food available measured in pounds per acre. Even if vegetation is abundant, there is a limit, called the satiation level, to the amount the animal will eat. The following table shows, for rabbits, the difference D between the satiation level and the amount A of food eaten for a variety of values of V. V=vegetaionlevel D=satiationlevel-A 27 0.16 36 0.12 89 0.07 134 0.05 245 0.01 a.Draw a plot of D versus V. b.Find an exponential function that approximates D. c.The satiation level of a rabbit is 0.18 pound per day. Use this, together with your work in part b, to find a formula for A. d.Find the vegetation level V for which the amount of food eaten by the rabbit will be 90 of its satiation level of 0.18 pound per day.arrow_forward
- Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Design Patents The following table shows the number P of design patents awarded by the U.S. Patents and Trademark Office from 1950 through 2010. t = years since 1950 P = patents 0 4718 10 2543 20 3214 30 3949 40 8024 50 17,413 60 22,799 a.Use exponential regression to model P as a function of t. b.Plot the data along with the regression equation. c.In what years were there more patents awarded than might be expected from the model?arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Gray Wolves in WisconsinGray wolves were among the first mammals protected under the Endangered Species Act in the 1970s. Wolves recolonized in Wisconsin beginning in 1980.Their population grew reliably after 1985 as follows: Year Wolves Year Wolves 1985 15 1993 40 1986 16 1994 57 1987 18 1995 83 1988 28 1996 99 1989 31 1997 145 1990 34 1998 178 1991 40 1999 197 1992 45 2000 266 a. Explain why an exponential model may be appropriate. b. Are these data exactly exponential? Explain. c. Find an exponential model for these data. d. Plot the data and the exponential model. e. Comment on your graph in part d. Which data points are below or above the number predicted by the exponential model?arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Postal RatesThe table below shows the cost s, in cents, of a domestic first-class postage stamp in the United States tyears after 1900. t=time,inyearssince1900 s=costofstamp 19 2 32 3 58 4 71 8 78 15 85 22 95 32 102 37 109 44 116 47 a.Use exponential regression to model s as an exponential function of t. b.What cost does your model give for a 1988 stamp? Report your answer to the nearest cent. The actual cost was 25cents. c.Plot the data and the exponential model.arrow_forward
- Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Medicare ExpendituresThe following table is from the Centers for Medicare that is, M=1000?arrow_forwardSpecial Rounding Instructions When you perform logistic regression, round the r value to three decimal places and the other parameters to two decimal places. Round all answers to two decimal places unless other-wise indicated. Magazine Sales Our new magazine initially sells 300 copies per month. Research indicates that a vigorous advertising campaign could increase sales by 20 each month if our market were unlimited. But research also indicates that magazine sales in our area are unlikely to exceed 1200 per month. Make a logistic model of projected magazine sales.arrow_forwardSpecial Rounding Instructions When you perform logistic regression, round the r value to three decimal places and the other parameters to two decimal places. Round all answers to two decimal places unless other-wise indicated. PTA Participation A school board has a plan to increase participation in the PTA. Currently only about 25 parents attend meetings. Suppose the school board plan results in logistic growth of attendance. The school board believes that its plan can eventually lead to an attendance level of 50 parents. In the absence of limiting factors, the school board believes that its plan can increase participation by 10 each month. Let m denote the number of months since the participation plan was put in place, and let P be the number of parents attending PTA meetings. a. What is the carrying capacity K for a logistic model of P versus m? b. Find the constant b for a logistic model. c. Find the r value for a logistic model. Round your answer to three decimal places. d. Find a logistic model for P versus m.arrow_forward
- Special Rounding Instructions. For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Caloric Content Versus Shell Length In 1965, Robert T.Paine gathered data on the length L, in millimeters, of the shell and the caloric content C, in calories, for a certain mollusk. The table below is adapted from those data. L=length C=Calories 7.5 92 13 210 20 625 24 1035 31 1480 a.Find an exponential model of calories as a function of length. b.Plot the graph of the data and the exponential model. Which of the data points show a good deal less caloric content than the model would predict for the given length? c.If length is increased by 1millimeter, how is caloric content affected?arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Choose the Model A car travels down a straight highway at a constant speed. Which is a better model for the distance traveled as a function of the time: linear or exponential?arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Cost of Scientific periodicals The table below shows the average cost C, in dollars, of chemistry and physics periodicals tyears after 1980. 29 t=yearssince1980 C=cost,indollars 0 140 5 250 10 410 15 780 20 1300 22 1520 a.Make an exponential model of C as a function of t. b.Plot the data and the exponential model. c.What was the yearly percentage growth rate of the cost of chemistry and physics periodicals? d.If this exponential trend continues, what will be the expected average cost of physics and chemistry periodicals in 2020? Round your answer to the nearest dollar.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning