Concept explainers
1–16 ■ Population Growth These exercises use the population growth model.
Bat Population The bat population in a certain Midwestern county was 350, 000 in 2012, and the observed doubling time for the population is 25 years.
(a) Find an exponential model
(b) Find an exponential model
(c) Sketch a graph of the population at time t.
(d) Estimate how long it takes the population to reach 2 million.
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Algebra and Trigonometry (MindTap Course List)
- Population Growth These exercises use the population growth model. 10. Bat Population The bat Population in a certain Midwestern county was 350,000in 2012. and the observed doubling tune for the is 25 years. (a) Find anexponential model n(t)=n0et/a for the Populationt years after 2012. (b) Find an exponential model n(t)=n0ert the Population t years after 2012. (c) Sketch a graph of the population at time t. (d)Estimate long it takes to reach 2 million.arrow_forwardBacteria Decay A lab culture initially contains 500 bacteria. Two hours later, the number of bacteria decreases to 200. Find the exponential decay model of the form B=B0akt that approximates the number of bacteria B in the culture after t hours.arrow_forward116 Population Growth These exercises use the population growth model. Bacteria Culture A certain culture of the bacterium Rhodo-bacter sphaeroides initially has 25 bacteria and is observed to double every 5 hours. a Find an exponential model n(t)=n02t/a for the number of bacteria in the culture after t hours. b Estimate the number of bacteria after 18 hours. c After how many hours will the bacteria count reach 1 million?arrow_forward
- 116 Population Growth These exercises use the population growth model. Bacteria Culture A certain culture of the bacterium Streptococcus A initially has 10 bacteria and is observed to double every 1.5 hours. a Find an exponential model n(t)=n02t/a for the number of bacteria in the culture after t hours. b Estimate the number of bacteria after 35 hours. c After how many hours will the bacteria count reach 10, 000?arrow_forwardPopulation 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_forwardLogistic Growth Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: p(t)=d1+kea Where c, d, and k are positive constants. For a certain fish population in a small pond d=1200, k=11, c=0.2, and t is measured in years. The fish were introduced into the pond at time t=0 . How many fish were originally put in the pond? Find the population after 10, 20, and 30 years. Evaluate p(t) for large values of t. What value does the population approach as t? Does the graph shown confirm your calculations?arrow_forward
- Population 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_forwardPopulation Growth These exercises use the population growth model. 2. Bacteria Culture A certain culture or the bacterium Rhodo-bacter sphaeroides initially has 25 bacteria and is to double every 5 hours. (a) Find an exponential model n(t)=n02t/a for the number of bacteria in the culture after t hours. (b) Estimate the number Of bacteria after 18 hours. (c) After how Will bacteria reach 1 million?arrow_forwardPopulation Growth These exercises use the population growth model. 1. Bacteria Culture A certain culture Of the bacterium Streptococcus A initially 10 and is to every 1.5 hours. (a) Find an exponential for the number of bacteria in culture after t hours. (b) Estimate the number of bacteria after 35 hours. (c) After how many hours will the bacteria count reach 10,000?arrow_forward
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