Question

there is a population of 20000 bacteria in a colony. if the number of bacteria doubles every 430 hours, what will the population be 860 from now?

Answer 1

The question has to do with exponential growth function

`\begin{gathered} \text{Let the expeonential growth function be } \\ p=p_{0^{}}e^(kt)------------(1) \\ \text{where p}_0=2000\text{ (initial population)} \\ t=430 \\ k=(\ln2)/(430) \\ k=0.001612 \end{gathered}`
`\begin{gathered} Putk=0.001612,p_o=2000\text{ into equation (1) above} \\ p=p_{0^{}}e^(kt) \\ p=2000e^(0.001612(t)) \\ p=2000e^(0.001612t) \\ \text{When the time t is 860 hours} \\ p=2000e^(0.001612(860)) \\ p=2000e^(1.38632) \\ p=2000(4) \\ p=8000 \end{gathered}`

Hence , the population after 860 hours will be 8000