# Question #74e81

Dec 14, 2017

3252 bacteria

#### Explanation:

At the start, $t = 0$, the initial number of bacteria (${N}_{0}$) is 2000. After 6 hours ($t = 6$), the number of bacteria ($N$) is now 2400.

Therefore, at $t = 6$, the following exponential equation can be formed (with some constant $k$).

$2400 = 2000 \cdot {e}^{6 k}$

Divide both sides by $2000$:

$1.2 = {e}^{6 k}$

Take the logs of both sides:

$\ln \left(1.2\right) = \ln \left({e}^{6 k}\right)$

Since $\ln \left({e}^{x}\right) = x$, this can be rephrased as:

$\ln \left(1.2\right) = 6 k$

$k = \ln \frac{1.2}{6} = 0.03038692613$

Going back to the original equation, we can find the number of bacteria at $t = 16$:

$N = 2000 \cdot {e}^{0.03038692613 \cdot 16}$ = 3252