Question

The number of bacteria P (t) in a certain population increases according to the following function, we’re time t is measured in hours.

Answer 1

Initial number: 3000 bacterias

Number after 6 hours: 8834 bacterias

Explanation:

We have the following function:

`P\mleft(t\mright)=3000\cdot e^(0.18t)`

(a) The initial number is when the time is equal to 0, therefore, we replace:

`\begin{gathered} P\mleft(0\mright)=3000\cdot\: e^(0.18\cdot0) \\ P(0)=3000\cdot1 \\ P(0)=3000 \end{gathered}`

(b) The number after 6 is when the time equals 6, therefore we replace:

`\begin{gathered} P\mleft(6\mright)=3000\cdot\: e^(0.18\cdot6) \\ P(6)=8834.03\cong8834 \end{gathered}`