Concept explainers
TEST YOUR UNTERSTANDING FOR EXAMPLE 2.12
Replace the growth formula in the example by
In forestry management, it is important to know the growth and the yield of a forest stand. The growth G is the amount by which the volume of wood will increase in a unit of time, and the yield Y is the total volume of wood. A forest manager has determined that in a certain stand of age A, the growth
And the yield
Here G is measured in cubic feet per acre per year, Y in cubic feet per acre, and A in years.
Part 1 Draw a graph of growth as a function of age that includes ages up to 60 years.
Part 2 At what age is growth maximized?
Trending nowThis is a popular solution!
Chapter 2 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Maria, a biologist is observing the growth pattern of a virus. She starts with 100 of the virus that grows at a rate of 10% per hour. She will check on the virus in 24 hours. How many viruses will she find?arrow_forwardFlood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forwardDecrease in Bacteria When an antibiotic is introduced into a culture of 50,000 bacteria, the number of bacteria decreases exponentially. After 9 hours, there are only 20,000 bacteria. Write an exponential equation to express the growth function y in terms of time t in hours. In how many hours will half the number of bacteria remain?arrow_forward
- Tracer Dye The amount of a tracer dye injected into the blood stream decrease exponentially, with a decay constant of 3 per minute. If 6 cc are present initially, how many cubic centimeters are present after 10 minutes? Here k will be negative.arrow_forwardWhat is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation. What does this point tell us about the population?arrow_forwardThe table shows the mid-year populations (in millions) of five countries in 2015 and the projected populations (in millions) for the year 2025. (a) Find the exponential growth or decay model y=aebt or y=aebt for the population of each country by letting t=15 correspond to 2015. Use the model to predict the population of each country in 2035. (b) You can see that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation y=aebt gives the growth rate? Discuss the relationship between the different growth rates and the magnitude of the constant.arrow_forward
- Use the table feature on a graphing calculator or a spreadsheet to develop a table that shows how much of the drug is present in a patients system at the end of each 1/2 hour time interval for 24 hours for the model found in Exercise 1a. A chart such as this provides the health care worker with immediate information about drug levels. Exercise: 1. A 500-mg dose of a drug is administered by rapid injection to a patient. The half-life of the drug is 9 hours. a. Find a model for the amount of drug in the bloodstream t hours after the drug is administered.arrow_forwardEastern Pacific Yellowfin Tuna Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded N=1481+36e2.61t where t is measured in years and N is measured in thousands of tons of fish. a. What is the r value for the Eastern Pacific yellowfin tuna? b. What is the carrying capacity K for the Eastern Pacific yellowfin tuna? c. What is the optimum yield level? d. Use your calculator to graph N versus t. e. At what time was the population growing the most rapidly?arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill