The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Which countries have a decreasing population? By what percentage is the population of these countries decreasing each Country B A = 1183 1e 0005t Country C A= 37.5 e 0019t A= 123 7 e -0.004t -0.003t A = 145.7 e year? Country D Country E Select the correct choice below and fill in the answer boxes to complete your choice. (Simplify your answers. Type integers or decimals rounded to the nearest tenth as needed.) O A. Country C and Country D have the decreasing populations The population of Country C is decreasing by % and the population of Country D is decreasing by % each year O B. Country B and Country D have the decreasing populations. The population of Country B is decreasing by % and the population of Country D is decreasing by % each year OC. Country B and Country C have the decreasing populations. The population of Country B is decreasing by % and the population of Country C is decreasing by % each year. O D. Country D and Country E have the decreasing populations. The population of Country D is decreasing by % and the population of Country E is decreasing by % each year.

The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Which countries have a decreasing population? By what percentage is the population of these countries decreasing each Country B A = 1183 1e 0005t Country C A= 37.5 e 0019t A= 123 7 e -0.004t -0.003t A = 145.7 e year? Country D Country E Select the correct choice below and fill in the answer boxes to complete your choice. (Simplify your answers. Type integers or decimals rounded to the nearest tenth as needed.) O A. Country C and Country D have the decreasing populations The population of Country C is decreasing by % and the population of Country D is decreasing by % each year O B. Country B and Country D have the decreasing populations. The population of Country B is decreasing by % and the population of Country D is decreasing by % each year OC. Country B and Country C have the decreasing populations. The population of Country B is decreasing by % and the population of Country C is decreasing by % each year. O D. Country D and Country E have the decreasing populations. The population of Country D is decreasing by % and the population of Country E is decreasing by % each year.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section4.6: Modeling With Exponential Functions

Problem 12E: 116 Population Growth These exercises use the population growth model. Frog Population Some...

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More on the Pacific Sardine This is a continuation of Example 5.1. In this exercise, we explore the Pacific sardine population further, using the model in Example 5.1. a. If the current level of the Pacific sardine population is 50,000 tons, how long will it take for the population to recover to the optimum growth level of 1.2milliontons? Suggestion: One way to solve this is to make a new logistic formula using K2.4, r0.338, and N(0)0.05. b. The value of r used in Example 5.1 ignores the effects of fishing. If fishing mortality is taken into account, then r drops to 0.215 per year with the carrying capacity still at 2.4milliontons. Answer the question in part a using this lower value of r. Note: The population estimate of 50,000 tons and the adjusted value of r are given in the paper by Murphy see footnote 3 on page 347. Murphy points out that factoring in the growth of the competing anchovy population makes the recovery times even longer, and he adds. "It is disconcerting to realize how slowly the population will recover to its level of maximum productivity ... even if fishing stops." Studies to fit a logistic model to the Pacific sardine population have yielded. N=241+239e0.338t where t is measured in years and N is measured in millions of tons of fish. Part 1 What is r for the Pacific sardine? Part 2 According to the logistic model, in the absence of limiting factors, what would be the annual percentage growth rate for the Pacific sardine? Part 3 What is the environmental carrying capacity K? Part 4 What is the optimum yield level? Part 5 Make a graph of N versus t. Part 6 At what time t should the population he harvested? Part 7 What portion of the graph is concave up? What portion is concave down?
116 Population Growth These exercises use the population growth model. Deer Population The graph shows the deer population in a Pennsylvania county between 2010 and 2014. Assume that the population grows exponentially. a What was the deer population in 2010? b Find a function that models the deer population t years after 2010. c What is the projected deer population in 2018? d Estimate how long it takes the population to reach 100, 000.
Cat Population The stray-cat population in a small towngrows exponentially. In 1999 the town had 30 stray cats, and the relative growth rate was15% per year. (a)Find a function thatmodels stray-cat populationn(t) after s years. (b)Find the projected population after 4 year. (c)Find the number of years required for the stray-cat population to reach 500.
Making ModelsIn Exercise S-1 through S-4, make an exponential model y(t) with the given properties. The initial value is 700, and the amount decays by 20 each period.
U.S. Population The U.S. Constitution requires a census every 10 years. The census data for 17902010 are given in the table. a Make a scatter plot of the data. b Use a calculator to find an exponential model for the data. c Use your model to predict the population at the 2020 census. d Use your model to estimate the population in 1965. Year Population in millions Year Population in millions Year Population in millions 1790 1800 1810 1820 1830 1840 1850 1860 3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 1870 1880 1890 1900 1910 1920 1930 1940 38.6 50.2 63.0 76.2 92.2 106.0 123.2 132.2 1950 1960 1970 1980 1990 2000 2010 151.3 179.3 203.3 226.5 248.7 281.4 308.7
SKILL BUILDING EXERCISES Logistic GrowthWhen we add the notation of car carrying capacity to the basic assumption leading to the exponential model, we get a different model. What is the name of this model?
TEST YOUR UNDERSTANDING | FOR EXAMPLE 4.10 The following table shows the estimated world population in millions tyears after 1750. t=time,inyearssince1750 0 50 100 150 200 250 W=population,inmillions 791 978 1262 1650 2519 6070 Make an exponential model for W as a function of t. One date from the table shows population much larger than that given by the exponential model. Which date is that?