Question

The relative growth rate of world population has been decreasing steadily in recent years. On the basis of this, some population models predict that world population will eventually stabilize at a level that the planet can support. One such logistic model is $$P(t)=\frac{73.2}{6.1+5.9 e^{-0.02 t}}$$ where $t=0$ is the year 2000 and population is measured in billions. a. What world population does this model predict for the year $2200 ?$ For $2300 ?$ b. Sketch a graph of the function $P$ for the years 2000 to 2500 . c. According to this model, what size does the world population seem to approach as time goes on?

          The relative growth rate of world population has been decreasing steadily in recent years. On the basis of this, some population models predict that world population will eventually stabilize at a level that the planet can support. One such logistic model is $$P(t)=\frac{73.2}{6.1+5.9 e^{-0.02 t}}$$ where $t=0$ is the year 2000 and population is measured in billions.
a. What world population does this model predict for the year $2200 ?$ For $2300 ?$
b. Sketch a graph of the function $P$ for the years 2000 to 2500 .
c. According to this model, what size does the world population seem to approach as time goes on?

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Added by Jocelyn S.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Lauren Shelton

01/26/2022

Step 1

2}{6.1 + 5.9e^{-0.02 \times 200}}$$ $$P(200) = \frac{73.2}{6.1 + 5.9e^{-4}}$$ $$P(200) = \frac{73.2}{6.1 + 5.9 \times 0.01832}$$ $$P(200) = \frac{73.2}{6.1 + 0.1079}$$ $$P(200) = \frac{73.2}{6.2079}$$ $$P(200) \approx 11.79 \text{ billion}$$ ** Show more…

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The relative growth rate of world population has been decreasing steadily in recent years. On the basis of this, some population models predict that world population will eventually stabilize at a level that the planet can support. One such logistic model is $$P(t)=\frac{73.2}{6.1+5.9 e^{-0.02 t}}$$ where $t=0$ is the year 2000 and population is measured in billions. a. What world population does this model predict for the year $2200 ?$ For $2300 ?$ b. Sketch a graph of the function $P$ for the years 2000 to 2500 . c. According to this model, what size does the world population seem to approach as time goes on?

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