Concept explainers
Logistic Growth The logistic growth model
represents the proportion of new cars with global positioning system
What proportion of new cars in
Determine the maximum proportion of new cars that have a
Using a graphing utility, graph
When will
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Precalculus
- The US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?arrow_forwardMaria, 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_forwardEarthquake the graph shows the vertical acceleration of the Ground from the 1994 Northridge earthquake in Los Angles, as measured by a seismograph. (Here t represents the time in seconds.) (a) At what time t did the earthquake first make noticeable movement of the Earth? (b) At what time t did the earthquakes seem to end? (c) At what time t was the maximum intensity of the earthquake list reachedarrow_forward
- A Population of Foxes A breeding group of foxes is introduced into a protected area, and the population growth follws a logistic pattern. After t years, the population of foxes is given by N=37.50.25+0.76t foxes. a. How many foxes were intorduced into the protected area? b. Make a graph of N versus t and explain in words how the populatoin of foxes increases with time. c. When will the fox population reach 100 individuals?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_forwardFocal Length A refracting telescope has a main lens, or objective lens, and a second lens, the eyepiece see Figure 3.42. For a given magnification M of the telescope, the focal length F of the objective lens is a linear function of the focal length Fe of the eyepiece. For example, a telescope with magnification M=80 times can be constructed using various combinations of lenses. The following table gives some samples of focal length for telescopes with magnification M=80. Here focal lengths are in centimeters. Fe 0.3 0.5 0.7 0.9 F 24 40 56 72 a. Construct a linear model for the data. b. In this example, the magnification M is 80. In general, F is proportional to Fe, and the constant of proportionality is M. Use this relation to write a formula for F in terms of Fe and M. c. Solve the equation you obtained in part b for M and thus obtain a formula for magnification as a function of objective lens focal length and eyepiece focal length. d. To achieve a large magnification, how should the objective and eyepiece lenses be selected? FIGURE 3.42arrow_forward
- Modeling Human Height with a Logistic Function A male child is 21inches long at birth and grows to an adult height of 73inches. In this exercise, we make a logistic model of his height as a function of age. a. Use the given information to find K and b for the logistic model. b. Suppose he reaches 95 of his adult height at age 16. Use this information and that from part a to find r. Suggestion: You will need to use either the crossing-graphs method or some algebra involving the logarithm. c. Make a logistic model for his height H, in inches, as a function of his age t, in years. d. According to the logistic model, at what age is he growing the fastest? e. Is your answer to part d consistent with your knowledge of how humans grow?arrow_forwardTable 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill