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In 1837 the Dutch mathematician Pierre François Verhulst proposed a different model for population growth given by the logistic equation $$P(t)=\frac{P_{0} k}{a P_{0}+\left(k-a P_{0}\right) e^{-k t}},$$where $P_{0}=P(0)$,Assume in this model, $k=0.029$ and $a=3.67 \times 10^{-12} .$ If the world population in 1960 was 3 billion. Predict the world population using this model in:(a) $1965,$ (b) $1970,$ (c) $1982,$ (d) $1950,$ (e) 1900 . (f) Letting $t$ get very large,approximate the limiting value of the world's population as predicted by this model. (Assume $t=0$ corresponds to 1960 .)

(a) 3.468 billion(b) 4.01 billion(c) 5.68 billion(d) 2.24 billion

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Missouri State University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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In $1751,$ Benjamin Frankl…

we are convinced that be off the equal 73 point toe upon 6.1 plus 5.90 days toe buying a 0.0 duty when the equals zero years 2000 on that every year I didn't do it. So the year 2200 is going to be d equals 200 the year 2300 is gonna be Do you implicitly we go toe the I 84 calculator and blood are function read. I cannot function so that's them Now we tap on the glass on Now we have to find the value for X equals 203 100 We go toe the Cal commando on the select value and their eggs equals 200. That gets us value as 11.79 billion on for X equals 300. That means proceed do we get the value of an X equals 300 as 11.97 billion. So we know down that in here 2200 the population with 11.79 billion on the year 2300 the population will be 11.97 billion for Part B. We have already drawn the craft for the years 2000 to 2500 so that is done. A now for part C. We can clearly see that the population model approaches this point using the graph so we go and knees do mode on, Gentry said. When times increasing the population grudges and it converges with value off good so the population will end up conversion at 12 billion.

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