Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN: 9781305071742
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Cengage Learning
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Textbook Question
Chapter 4.6, Problem 12E
1–16 ■ Population Growth These exercises use the population growth model.
Frog Population Some bullfrogs were introduced into a small pond. The graph shows the bullfrog population for the next few years. Assume that the population grows exponentially.
(a) What was the initial bullfrog population?
(b) Find a function that models the bullfrog population t years since the bullfrogs were put into the pond.
(c) What is the projected bullfrog population after 15 years?
(d) Estimate how long it takes the population to reach 75, 000.
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Chapter 4 Solutions
Algebra and Trigonometry (MindTap Course List)
Ch. 4.1 - The function f(x)=5x is an exponential function...Ch. 4.1 - Prob. 2ECh. 4.1 - a To obtain the graph of g(x)=2x1, we start with...Ch. 4.1 - In the formula A(t)=P(1+rn)nt for compound...Ch. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10E
Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - 2124 Exponential Functions from a Graph Find the...Ch. 4.1 - 2124 Exponential Functions from a Graph Find the...Ch. 4.1 - 2526 Exponential Functions from a Graph Match the...Ch. 4.1 - 2526 Exponential Functions from a Graph Match the...Ch. 4.1 - 2740 Graphing Exponential Functions Graph the...Ch. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - 4546 Comparing Exponential and Power Functions In...Ch. 4.1 - 4546 Comparing Exponential and Power Functions In...Ch. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - 5152 Difference Quotients These exercises involve...Ch. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Compound Interest If 4000 is borrowed at a rate of...Ch. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - 34 Evaluating Exponential Functions Use a...Ch. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Hyperbolic sine Function The hyperbolic sine...Ch. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Medical Drugs When a certain medical drug is...Ch. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Mixtures and concentrations A 50-gal barrel is...Ch. 4.2 - Logistic Growth Animal populations are not capable...Ch. 4.2 - Bird Population The population of a certain...Ch. 4.2 - Prob. 29ECh. 4.2 - Tree Diameter For a certain type of tree the...Ch. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.3 - logx is the exponent to which the base 10 must be...Ch. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - 78 Logarithmic and Exponential forms Complete the...Ch. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - 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Prob. 66ECh. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Wealth Distribution Vilfredo Pareto (18481923)...Ch. 4.4 - Prob. 74ECh. 4.4 - Magnitude of Stars The magnitude M of a star is a...Ch. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.5 - Lets solve the exponential equation 2ex=50. a...Ch. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - 1138 Exponential Equations a Find the exact...Ch. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - 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Prob. 86ECh. 4.5 - Prob. 87ECh. 4.5 - Prob. 88ECh. 4.5 - Prob. 89ECh. 4.5 - Prob. 90ECh. 4.5 - Prob. 91ECh. 4.5 - Prob. 92ECh. 4.5 - Prob. 93ECh. 4.5 - Prob. 94ECh. 4.5 - Prob. 95ECh. 4.5 - Prob. 96ECh. 4.5 - Fish Population A small lake is stocked with a...Ch. 4.5 - Prob. 98ECh. 4.5 - Prob. 99ECh. 4.5 - Cooling an Engine Suppose youre driving your car...Ch. 4.5 - Electric circuits An electric circuit contains a...Ch. 4.5 - Learning Curve A learning curve is a graph of a...Ch. 4.5 - Prob. 103ECh. 4.5 - Prob. 104ECh. 4.5 - Prob. 105ECh. 4.6 - 116 Population Growth These exercises use the...Ch. 4.6 - 116 Population Growth These exercises use the...Ch. 4.6 - Prob. 3ECh. 4.6 - Prob. 4ECh. 4.6 - Prob. 5ECh. 4.6 - Prob. 6ECh. 4.6 - Prob. 7ECh. 4.6 - Prob. 8ECh. 4.6 - Prob. 9ECh. 4.6 - 116 Population Growth These exercises use the...Ch. 4.6 - 116 Population Growth These exercises use the...Ch. 4.6 - 116 Population Growth These exercises use the...Ch. 4.6 - 116 Population Growth These exercises use the...Ch. 4.6 - Prob. 14ECh. 4.6 - 116 Population Growth These exercises use the...Ch. 4.6 - Prob. 16ECh. 4.6 - Prob. 17ECh. 4.6 - Prob. 18ECh. 4.6 - Prob. 19ECh. 4.6 - Prob. 20ECh. 4.6 - Prob. 21ECh. 4.6 - Prob. 22ECh. 4.6 - Prob. 23ECh. 4.6 - Prob. 24ECh. 4.6 - 2528 Law of Cooling These exercises use Newtons...Ch. 4.6 - 2528 Law of Cooling These exercises use Newtons...Ch. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.7 - Prob. 1ECh. 4.7 - Prob. 2ECh. 4.7 - Ion Concentration The pH reading of a sample of...Ch. 4.7 - Prob. 4ECh. 4.7 - Prob. 5ECh. 4.7 - Prob. 6ECh. 4.7 - pH of Wine If the pH of a wine is too high, say,...Ch. 4.7 - pH of Saliva The pH of saliva is normally in the...Ch. 4.7 - 9. Earthquake Magnitude and Intensity a Find the...Ch. 4.7 - Prob. 10ECh. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - Prob. 13ECh. 4.7 - Prob. 14ECh. 4.7 - Prob. 15ECh. 4.7 - Prob. 16ECh. 4.7 - Prob. 17ECh. 4.7 - Prob. 18ECh. 4.7 - Hearing Loss from MP3 Players Recent research has...Ch. 4.7 - Prob. 20ECh. 4.7 - Prob. 21ECh. 4.CR - Let f be the exponential function with base a. a...Ch. 4.CR - Prob. 2CCCh. 4.CR - Prob. 3CCCh. 4.CR - Prob. 4CCCh. 4.CR - Prob. 5CCCh. 4.CR - Prob. 6CCCh. 4.CR - Prob. 7CCCh. 4.CR - Prob. 8CCCh. 4.CR - Prob. 9CCCh. 4.CR - Prob. 10CCCh. 4.CR - Prob. 11CCCh. 4.CR - Prob. 12CCCh. 4.CR - Suppose that the initial mass of radioactive...Ch. 4.CR - Prob. 14CCCh. 4.CR - Prob. 15CCCh. 4.CR - Prob. 16CCCh. 4.CR - Prob. 17CCCh. 4.CR - Prob. 18CCCh. 4.CR - Prob. 1ECh. 4.CR - Prob. 2ECh. 4.CR - Prob. 3ECh. 4.CR - Prob. 4ECh. 4.CR - Prob. 5ECh. 4.CR - Prob. 6ECh. 4.CR - Prob. 7ECh. 4.CR - Prob. 8ECh. 4.CR - Prob. 9ECh. 4.CR - Prob. 10ECh. 4.CR - Prob. 11ECh. 4.CR - Prob. 12ECh. 4.CR - Prob. 13ECh. 4.CR - Prob. 14ECh. 4.CR - Prob. 15ECh. 4.CR - Prob. 16ECh. 4.CR - Prob. 17ECh. 4.CR - Prob. 18ECh. 4.CR - Prob. 19ECh. 4.CR - Prob. 20ECh. 4.CR - Prob. 21ECh. 4.CR - Prob. 22ECh. 4.CR - Prob. 23ECh. 4.CR - Prob. 24ECh. 4.CR - Prob. 25ECh. 4.CR - Prob. 26ECh. 4.CR - 2528 Logarithmic Form Write the equation in...Ch. 4.CR - Prob. 28ECh. 4.CR - Prob. 29ECh. 4.CR - Prob. 30ECh. 4.CR - Prob. 31ECh. 4.CR - Prob. 32ECh. 4.CR - Prob. 33ECh. 4.CR - Prob. 34ECh. 4.CR - Prob. 35ECh. 4.CR - Prob. 36ECh. 4.CR - Prob. 37ECh. 4.CR - Prob. 38ECh. 4.CR - Prob. 39ECh. 4.CR - Prob. 40ECh. 4.CR - Prob. 41ECh. 4.CR - Prob. 42ECh. 4.CR - Prob. 43ECh. 4.CR - Prob. 44ECh. 4.CR - Prob. 45ECh. 4.CR - Prob. 46ECh. 4.CR - Prob. 47ECh. 4.CR - Prob. 48ECh. 4.CR - Prob. 49ECh. 4.CR - Prob. 50ECh. 4.CR - Prob. 51ECh. 4.CR - Prob. 52ECh. 4.CR - Prob. 53ECh. 4.CR - Prob. 54ECh. 4.CR - Prob. 55ECh. 4.CR - Prob. 56ECh. 4.CR - Prob. 57ECh. 4.CR - Prob. 58ECh. 4.CR - Prob. 59ECh. 4.CR - Prob. 60ECh. 4.CR - Prob. 61ECh. 4.CR - Prob. 62ECh. 4.CR - Prob. 63ECh. 4.CR - Prob. 64ECh. 4.CR - Prob. 65ECh. 4.CR - Prob. 66ECh. 4.CR - Prob. 67ECh. 4.CR - Prob. 68ECh. 4.CR - Prob. 69ECh. 4.CR - Prob. 70ECh. 4.CR - Prob. 71ECh. 4.CR - Prob. 72ECh. 4.CR - Prob. 73ECh. 4.CR - Prob. 74ECh. 4.CR - Prob. 75ECh. 4.CR - Prob. 76ECh. 4.CR - Prob. 77ECh. 4.CR - 7578 Local Extrema and Asymptotes Draw a graph of...Ch. 4.CR - Prob. 79ECh. 4.CR - Prob. 80ECh. 4.CR - Prob. 81ECh. 4.CR - Prob. 82ECh. 4.CR - Prob. 83ECh. 4.CR - Prob. 84ECh. 4.CR - Prob. 85ECh. 4.CR - Prob. 86ECh. 4.CR - 8588 Change of Base Use the Change of Base...Ch. 4.CR - Prob. 88ECh. 4.CR - Prob. 89ECh. 4.CR - Prob. 90ECh. 4.CR - Prob. 91ECh. 4.CR - Prob. 92ECh. 4.CR - Prob. 93ECh. 4.CR - Prob. 94ECh. 4.CR - Prob. 95ECh. 4.CR - Prob. 96ECh. 4.CR - Prob. 97ECh. 4.CR - Bacterial Growth A culture contains 10,000...Ch. 4.CR - Prob. 99ECh. 4.CR - Radioactive Decay A sample of bismuth-210 decayed...Ch. 4.CR - Radioactive Decay The half-life of radium-226 is...Ch. 4.CR - Prob. 102ECh. 4.CR - Bird Population The graph shows the population of...Ch. 4.CR - Prob. 104ECh. 4.CR - Prob. 105ECh. 4.CR - Prob. 106ECh. 4.CR - Prob. 107ECh. 4.CR - Decibel Scale The drilling of a jackhammer was...Ch. 4.CT - Sketch the graph of each function, and state its...Ch. 4.CT - Find the domain of the function. a f(t)=ln(2t3) b...Ch. 4.CT - Prob. 3CTCh. 4.CT - Prob. 4CTCh. 4.CT - Prob. 5CTCh. 4.CT - Prob. 6CTCh. 4.CT - Prob. 7CTCh. 4.CT - Prob. 8CTCh. 4.CT - Prob. 9CTCh. 4.CT - Prob. 10CTCh. 4.CT - Prob. 11CTCh. 4.CT - The half-life of krypton-91(91Kr) is 10 s. At time...Ch. 4.CT - An earthquake measuring 6.4 on the Richter scale...Ch. 4.FOM - U.S. Population The U.S. Constitution requires a...Ch. 4.FOM - A Falling Ball In a physics experiment a lead ball...Ch. 4.FOM - Half-Life of Radioactive Iodine A student is...Ch. 4.FOM - The Beer-Lambert Law As sunlight passes through...Ch. 4.FOM - Prob. 5PCh. 4.FOM - Prob. 6PCh. 4.FOM - Prob. 7PCh. 4.FOM - Prob. 8PCh. 4.FOM - Prob. 9PCh. 4.FOM - Prob. 10P
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- Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.arrow_forward116 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.arrow_forwardPopulation Growth These exercises use the population growth model. 3. Squirrel Population A grey squirrel population was intro-duced in a certain county or Great Britain 30 years ago. Biologists observe that thepopulation double every 6 years, and now population is 100,000. (a) What was the initial size Of the squirrel population? (b) Estimate the squirrel population 10 years from now. (e) Sketch a graph of the squirrel population.arrow_forward
- 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 deer Population in 2010? (b) Find a function that model the deer population t years after 2010. (c) What is the projected population in 2018? (d) Estimate how long it takes the population to reach 100,000.arrow_forwardPopulation Growth These exercises use the population growth model. Frog Population Some bullfrogs were into a small pond. TIE graph bullfrog.population for the next few years. Assume that the population grows (a) What was the initial bullfrog population? (b) Find a function that models the bullfrog Bypopulation t yeas since the bullfrogs were put into pond. (c) What is the projected bullfrogpopulation after 15 years? (d) Estimate how long it takes the population to reach 75,000.arrow_forwardU.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 151.3 179.3 203.3 226.5 248.7 281.4 308.7arrow_forward
- Population Growth These exercises use the population growth model. 4. Bird Population A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 13,000. (a) What was initial size Of the bird population? (b) Estimate the bird 5 years from now. (c) Sketch a graph Of the birdarrow_forwardGrowth Rate Versus Weight Ecologists have studied how a populations intrinsic exponential growth rate r is related to the body weight W for herbivorous mammals. In table 5.2, W is the adult weight measured in pounds, and r is growth rate per year. Animal Weight W r Short-tailed vole 0.07 4.56 Norway rat 0.7 3.91 Rue deer 55 0.23 White-tailed deer 165 0.55 American elk 595 0.27 African elephant 8160 0.06 Find a formula that models r as a power function of W, and draw a graph of this function.arrow_forwardModeling 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_forward
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