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A country's population in 1990 was 37 million. in 1999 it was 40 million. estimate the population in 2016 using the exponential growth formula. round your answer to the nearest million
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Jul 21, 2018
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A country's population in 1990 was 37 million. in 1999 it was 40 million. estimate the population in 2016 using the exponential growth formula. round your answer to the nearest million
Mathematics
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Cphill
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1. The exponential growth formula that predicts the growth of population as a function of years y is:
where
is the initial population, and k is the growth rate.
2. So we predict the population in 2016 to be
We need to find P_o, and also the growth factor k.
e is approximately
2.718, multiply it 9 times to get e^9: 8095.53
so
then
whose value is 0.0087, using a scientific calculator or logarithm calculator online.
Now,
so
3.
=46.35 million
Forefinger
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Jul 23, 2018
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Forefinger
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This is the concept of application of exponential growth, suppose in 1990 time,t=0 and in 1990 time,t=9. Using the exponential growth formula given by:
f(t)=ae^(kt)
thus substituting the value we get:
40=37e^(9k)
this can be written as:
(40/37)=e^(9k)
introducing the natural logs we get:
ln(40/37)=9k
hence;
k=1/9ln(40/37)=0.0087
Therefore our formual will be given by:
f(t)=37e^(0.0087t)
N/B: The population is in millions. Thus to get the population in 2016 we shall proceed as follows;
t=26
thus
f(t)=37e^(26*0.0087)
f(t)=46.35 million
Liam Allan
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Jul 25, 2018
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Liam Allan
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