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

\[ P(t) = P_0 \cdot 2^{\frac{t}{d}} \]

where \( P(t) \) is the population after \( t \) hours, \( P_0 \) is the initial population, \( t \) is the time in hours, and \( d \) is the doubling time, what is the population of bacteria in the culture after 14 hours, to the nearest whole number?

Answer :

Answer:

Population of bacteria in culture after 14 hours is 285541.

Step-by-step explanation:

We are given with [tex]P_{t} =P_{0}(2)^{\frac{d}{t}}[/tex]

Here initial population is 41000 , t=5 and d=14

Plug in these values into the formula

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

Simplify

[tex]P_{14}= 41000(2)^{2.8}[/tex]

=41000(6.9644)

=285540.5847...

To the nearest whole number is 285541.

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Rewritten by : Barada

Answer:

285541.

Step-by-step explanation:

P0=41000-The initial population

t=14-Time elapsed

d=5-The doubling time

Pt=P0⋅2^t/d

Pt=41000⋅2^14/5-Plug in

Pt=285540.5848≈285541-(Use parenthesis in the calculator for the exponent)