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Answer :
The population of bacteria in the culture after 13 hours is approximately 43,389.
We can find the population of bacteria after 13 hours by following these steps:
Identify the given values:
p₀ (initial population) = 400
t (time) = 13 hours
d (doubling time) = 2 hours
Fill in the formula:
pₜ = p₀ ⋅ 2^(t/d)
pₜ = 400 ⋅ 2^(13/2)
Calculate the exponent:
13/2 = 6.5
Raise 2 to the calculated exponent:
2^(6.5) ≈ 108.47
Multiply the initial population by the result:
pₜ = 400 ⋅ 108.47 ≈ 43388.8
Round the answer to the nearest whole number:
pₜ ≈ 43389
Therefore, the population of bacteria in the culture after 13 hours is approximately 43,389.
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