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A culture of bacteria has an initial population of 41,000 bacteria and doubles every 5 hours.

Using the formula [tex]P_t = P_0 \cdot 2^{\frac{t}{d}}[/tex], where:
- [tex]P_t[/tex] is the population after [tex]t[/tex] hours,
- [tex]P_0[/tex] is the initial population,
- [tex]t[/tex] is the time in hours,
- [tex]d[/tex] is the doubling time,

What is the population of bacteria in the culture after 14 hours?

Answer :

Answer:

285541

Step-by-step explanation:

According To The Question,

  • Given, A culture of bacteria has an initial population of 41000 bacteria and doubles in every 5 hours & [tex]P_{t} = P_{i}*(2)^{\frac{d}{t} }[/tex] .

Now, for the population of bacteria in the culture after 14 hours is [tex]P_{t}[/tex] . We have Initial Population([tex]P_{i}[/tex])=41000 , d=14 & t=5 .

Put These Value in Above Formula, We get

[tex]P_{t} = 41000*(2)^{\frac{14}{5} }[/tex]

[tex]P_{t} = 41000*2^{2.8}[/tex]

[tex]P_{t} = 41000*(6.9644)[/tex]

[tex]P_{t} =[/tex] 285540.5847 ≈ 285541

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