Question

A culture of bacteria has an initial population of 650 bacteria and doubles every 9 hours. Using the formula Pt=P0⋅2tdP_t = P_0\cdot 2^{\frac{t}{d}} P ​t ​​=P ​0 ​​⋅2 ​ ​d ​ ​t ​​ ​​, where PtP_t P ​t ​​ is the population after t hours, P0P_0 P ​0 ​​ is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 10 hours, to the nearest whole number?

Answer 1

So is doubling, first off, meaning, if the current amount say P, then when it doubles is 2P, or double that, or P + P, so the rate of growth is 100%, since it's doubling.

and is doing it every 9 hour cycle, thus

$\bf \textit{Periodic/Cyclical Exponential Growth}\\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &650\\ r=rate\to 100\%\to \frac{100}{100}\to &1.00\\ t=\textit{elapsed time}\to &10\\ c=period\to &9 \end{cases} \\\\\\ A=650(1 + 1)^{\frac{10}{9}}\implies A=650(2)^{\frac{10}{9}}\implies A=650\sqrt[9]{2^{10}}$