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Answer :
Final answer:
The population of the bacteria culture after 13 hours is approximately 590 bacteria when rounded to the nearest whole number, using the provided formula for exponential growth and the given doubling time.
Explanation:
The student has asked to calculate the population of bacteria in a culture after 13 hours given that the initial population is 230 bacteria and they double every 9 hours. We can use the provided exponential growth formula Pt = P₀ · 2t/d, where Pt is the population after t hours, P₀ is the initial population, t is the time in hours, and d is the doubling time in hours.
To find the population after 13 hours, we plug the values into the formula as follows:
Pt = 230 · 213/9
Calculating the exponent first, we get:
213/9 ≈ 2.565
Then, multiplying this by the initial population:
Pt ≈ 230 · 2.565
Pt ≈ 589.95
So, the population of bacteria after 13 hours is 590 to the nearest whole number.
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