Use the exponential growth model #P(t) = P_0e^(kt)#. How long will it take for the population of a certain country to double if its annual growth rate is 3.5%?

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Answer 1 · 2016-08-01T21:30:20

20.15 years to 2 dp

Let's assume the units of t are years. We want to find k.

#P(1) = 1.035P_0 = P_0e^k#

#e^k = 1.035#

#lne^k = ln(1.035)#

#kln(e) = ln(1.035)#

#implies k = ln(1.035)yr^(-1)#

Now need #P(t) = 2P_0#

#2P_0 = P_0e^(kt)#

#e^(kt) = 2#

#kt = ln(2)#

#t = ln(2)/k = ln(2)/ln(1.035)#

#t = 20.15# years