POPULATION GROWTH A conservation organiza- tion releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 1000 animals and that the growth of the pack will be modeled by the logistic curve 1000 p() 1+ 9e¯0.16564 where t is measured in months (see figure). 1200 1000+ 800+ 600+ 400 200 2 4 6 8 10 12 14 16 18 Time (in months) (a) Estimate the population after 5 months. (b) After how many months will the population be 500? (c) Use a graphing utility to graph the function. Use the graph to determine the horizontal asymptotes, and interpret the meaning of the asymptotes in the context of the problem. Endangered species population

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61. POPULATION GROWTH A conservation organiza-
tion releases 100 animals of an endangered species into
a game preserve. The organization believes that the
preserve has a carrying capacity of 1000 animals and
that the growth of the pack will be modeled by the
logistic curve
1000
p(t)
1 + 9e¯0.16561
where t is measured in months (see figure).
P
1200
1000
800
600
400 -
200
4
6.
8 10 12 14 16 18
Time (in months)
(a) Estimate the population after 5 months.
(b) After how many months will the population be 500?
(c) Use a graphing utility to graph the function. Use the
graph to determine the horizontal asymptotes, and
interpret the meaning of the asymptotes in the
context of the problem.
Endangered
species population
Transcribed Image Text:61. POPULATION GROWTH A conservation organiza- tion releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 1000 animals and that the growth of the pack will be modeled by the logistic curve 1000 p(t) 1 + 9e¯0.16561 where t is measured in months (see figure). P 1200 1000 800 600 400 - 200 4 6. 8 10 12 14 16 18 Time (in months) (a) Estimate the population after 5 months. (b) After how many months will the population be 500? (c) Use a graphing utility to graph the function. Use the graph to determine the horizontal asymptotes, and interpret the meaning of the asymptotes in the context of the problem. Endangered species population
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