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# Continuously compounded rate

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14. The world population of Ferrets has increased at a continuously compounded rate from 20 in 1970 to about 60 in 2000. Develop a mathematical model to forecast population growth in future years.

a) Graph the population against time and determine, identify or describe this relationship in your own words. What is the effective percentage rate of growth?

b) Find (or estimate) the number of births (instantaneous rate of change) in 2009 and use this value to estimate the population in 2010.

c) When will the world population double to 120 and what is the average increase per year over this period?

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The solution develops a mathematical model to forecast population growth in future years.

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14. The world population of Ferrets has increased at a continuously compounded rate from 20 in 1970 to about 60 in 2000. Develop a mathematical model to forecast population growth in future years.

Mathematical Model: Nt= No e^rt
Where
Nt= Population at time t
N0= Population at time 0
t = Number of years since 1970 (Year 0)
r= rate of increase

We have to estimate the value of r using the data

For 1970, N0= 20, t=0
For 2000, t= 2000-1970 =30, N30= 60,

For 1970, 20= No e^(r x 0) = No
Thus No = 20
And Nt= 20 e^rt

For 2000, 60= 20 e^(r x 30)
Or, 3= e^(r x 30)
Taking natural logs of both sides,
ln 3 = ...

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