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

Aug 5, 2016

$Q = 3000 \left({2}^{\frac{t}{3}}\right)$

#### Explanation:

Let $q = C {e}^{k t}$.

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

Also, when t = 3 units of time,$Q = 6000 = 3000 {e}^{3 k}$

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

An elegant form for the growth model is

$Q = 3000 {e}^{\left(\frac{t}{3}\right) \ln 2} = 3000 {\left({e}^{\ln} 2\right)}^{\frac{t}{3}} = 3000 {\left(2\right)}^{\frac{t}{3}}$

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