Reminder Round all answers to two decimal places unless otherwise indicated.
Sales Growth A study of the sales
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a. What level of sales will be attained in the long run?
b. What is the largest rate of growth in sales?
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Growth in Length of Haddock D.S. Raitt found that the length L of haddock in centimeters as a function of the age t in years is given approximately by the formula L=5342.820.82t a. Calculate L(4) and explain what it means. b. Compare the average yearly rate of growth in length from age 5 to age 10 years with the average yearly rate of growth from age 15 to age 20 years. Explain in practical terms what this tells you about the way haddock grow. c. What is the longest haddock you would expect to find anywhere?arrow_forwardThe American Food Dollar The following table shows the percentage P=P(d) of the American food dollar that was spent on eating away from home at restaurants, for example as function of the date d. d=Year P=Precentspentawayfromhome 1969 25 1989 30 2009 34 a. Find P(1989) and explain what it means. b. What does P(1999) mean? Estimate its value. c. What is the average rate of change per year in percentage of the food dollar spent away from home for the period from 1989 to 2009? d. What does P(2004) mean? Estimate its value. Hint: Your calculation in part c should be useful. e. Predict the value of P(2014) and explain how you made your estimate.arrow_forwardRound all answers to two decimal places. InflationDuring a certain period, the price of a bag of groceries grows by about 3 each year. Which regression model should be used to approximate the price of a bag of groceries as a function of time: linear or exponential?arrow_forward
- Population Growth and Decline The table gives the population in a small coastal community for the period 1997-2006. Figures shown arc for January 1 in each year. (a) What was the average rate of change of population between 1998 and 2001? (b) What was the average rate of change of population between 2002 and 2004? (C) For what period of lime was the population increasing? (d) For what period of time was the population decreasing?arrow_forwardRound all answers to two decimal places unless otherwise indicated. 24. Timber Stumpage Price The following table shows timber stumpage prices for pine pulpwood in two regions of the American South. Prices are in dollars per ton and were recorded at the start of the indicated year. Year Southeast Mid-Atlantic 2002 6.50 4.00 2005 7.50 6.70 2007 7.00 10.00 a. For the Mid-Atlantic, what is the average rate of change per year in price from 2002 to 2005? b. Use your answers to part a to estimate the price in the Mid-Atlantic region at the start of 2004. The actual price was 6.40 per ton. c. For the southeast, what is the average rate of change per year in price form 2005 to 2007? d. Use your answer to part c to estimate the price in the Southeast at the start of 2008. e. For each region, find the percentage increase in price from 2002 to 2007. f. On the basis of your answer to part e, in the absence of other factors, would an investor in timber be better advised to choose the Southeast or the Mid-Atlantic?arrow_forwardMarine Fishery One class of models for population growth rates in marine fisheries assumes that the harvest from fishing is proportional to the population size. For one such model, we have G=0.3n(1n2)0.1n Here G is the growth rate of the population, in millions of tons of fish per year, and n is the population size, in millions of tons of fish. a.Make a graph of G versus n. include values of n up to 1.5 million tons. b.Use functional notation to express the growth rate if the population size is 0.24 million tons, and then calculate that value. c. Calculate G1.42 and explain in practical terms what your answer means. d.At what population size is the growth rate the largest?arrow_forward
- Titanic At 2:00 p.m. on April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 p.m. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approximately 3400-mile trip. (a) What was the total duration of the voyage in hours? (b) What was the average speed in miles per hour? (c) Write a function relating the distance of the Titanic from New York City and the number of hours traveled. Find the domain and range of the function. (d) Graph the function in part (c).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. National Health Care SpendingThe following table shows national health care costs, measured in billions of dollars. Date 1970 1980 1990 2000 2010 Costs, in billions 75 253 714 1353 2570 a.Plot the data. b.Find an exponential function that approximates the data for health care costs. c.By what percentage per year were national health care costs increasing during the period from 1970 through 2010? d.Use functional notation to express how much money was spent on health care in the year 2011, and then estimate that value.arrow_forward
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