# The number of bacteria in a culture grew from 275 to 1135 in three hours. How do you find the number of bacteria after 7 hours and Use the exponential growth model: A = A_0e^(rt)?

Aug 8, 2016

$\approx 7514$

#### Explanation:

$A = {A}_{0} {e}^{r t}$

$t$ in hours. ${A}_{0} = 275$. $A \left(3\right) = 1135$.

$1135 = 275 {e}^{3 r}$

$\frac{1135}{275} = {e}^{3 r}$

Take natural logs of both sides:

$\ln \left(\frac{1135}{275}\right) = 3 r$

$r = \frac{1}{3} \ln \left(\frac{1135}{275}\right) h {r}^{- 1}$

$A \left(t\right) = {A}_{0} {e}^{\frac{1}{3} \ln \left(\frac{1135}{275}\right) t}$

I'm assuming that it's just after 7 hours, not 7 hours following the initial 3.

$A \left(7\right) = 275 \cdot {e}^{\frac{7}{3} \ln \left(\frac{1135}{275}\right)} \approx 7514$