High School

A culture of bacteria has an initial population of 230 bacteria and doubles every 9 hours. Using the formula [tex]P_t = P_0 \cdot 2^{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, and [tex]d[/tex] is the doubling time, what is the population of bacteria in the culture after 13 hours, to the nearest whole number?

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.

Other Questions