Question
Asked Oct 30, 2019
8. In 1950, the world population was 2560 million people. In 1960, the population was
3040 million people. Assume that world population grows in constant relative propor-
tion
(a) What is the relative growth rate, k?
(b) Use the model to predict the population in 2020.
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8. In 1950, the world population was 2560 million people. In 1960, the population was 3040 million people. Assume that world population grows in constant relative propor- tion (a) What is the relative growth rate, k? (b) Use the model to predict the population in 2020.

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Expert Answer

Step 1

Consider P(t) is the population in the year t.

Let 0 is corresponds in the year 1950
From the given, P(0)=2560 and P(10) 3040
(a) The model is given by P(t) P(0)e*
P(t) 2560e
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Let 0 is corresponds in the year 1950 From the given, P(0)=2560 and P(10) 3040 (a) The model is given by P(t) P(0)e* P(t) 2560e

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Step 2

At t=10,...

P(10) 2560e*10
3040 2560e10k
3040
e10k
2560
3040
In(el0) In
10k
2560
(0.171)
k
10
k 0.0171
0.0171t
That is, the relative growth is P(t)= 2560e'
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P(10) 2560e*10 3040 2560e10k 3040 e10k 2560 3040 In(el0) In 10k 2560 (0.171) k 10 k 0.0171 0.0171t That is, the relative growth is P(t)= 2560e'

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