Population y grows according to the equation dy/dx=ky, where k is constant and t is measured in years. If the population doubles every 10 years, then what is the value of k?

1 Answer
Barry H.
Mar 4, 2018

#K=ln2/10#

Explanation:

Standard equation for 'the law of natural growth' is #P[t]=Ce^[kt#.

Let#P[t]=1# when # t=0#, and so #1=Ce^[k[0],# ie #C=1#

So when the population has doubled to #2#,

#2=e^[10k#, taking logs of of both sides ln#2=ln[e^[10k#]

ln#2=10k# [Theory of logs] therefore #k=ln2/[10]#. Hope this was helpful.

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