How do you find the associated exponential growth model: Q = 3,000 when t = 0; doubling time = 3?

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Answer 1 · 2016-08-05T02:21:27

#Q=3000(2^(t/3))#

Let # q = C e^(kt)#.

Then, as Q = 3000 when t = 0, C = 3000.

Also, when t = 3 units of time,# Q = 6000=3000e^(3k)#

So, #e^(3k)=2#, and so, #k = (1/3) ln 2=0.231, nearly.

An elegant form for the growth model is

#Q = 3000e^((t/3)ln 2)=3000(e^ln 2)^(t/3)=3000 (2)^(t/3)#

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