ANSWER:
Initial number: 3000 bacterias
Number after 6 hours: 8834 bacterias
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]P\mleft(t\mright)=3000\cdot e^{0.18t}[/tex]
(a) The initial number is when the time is equal to 0, therefore, we replace:
[tex]\begin{gathered} P\mleft(0\mright)=3000\cdot\: e^{0.18\cdot0} \\ P(0)=3000\cdot1 \\ P(0)=3000 \end{gathered}[/tex]
(b) The number after 6 is when the time equals 6, therefore we replace:
[tex]\begin{gathered} P\mleft(6\mright)=3000\cdot\: e^{0.18\cdot6} \\ P(6)=8834.03\cong8834 \end{gathered}[/tex]
