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

The Number Of Bacteria P T In A Certain Population Increases According To The Following Function Were Time T Is Measured In Hours class=

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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]

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