Question

A culture of bacteria has an initial population of 2900 bacteria and doubles every 5 hours. Using the 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, what is the population of bacteria in the culture after 13 hours, rounded to the nearest whole number?

Answer 1

Using the exponential growth formula with an initial population of 2900 bacteria that doubles every 5 hours, the population after 13 hours is calculated to be approximately 18,298 bacteria.

Step-by-step explanation:

To calculate the population of bacteria in the culture after 13 hours, we need to use the provided exponential growth formula, Pt = P0 ·2t/d, where:

• Pt is the final population after time t.
• P0 is the initial population.
• t is the time in hours.
• d is the doubling time in hours.

In this scenario, P0 is 2900 bacteria, t is 13 hours, and d is 5 hours (since the bacteria population doubles every 5 hours). Plugging these values into the formula, we get:

Pt = 2900 · 213/5

Compute the exponent first:

13/5 = 2.6

Now, calculate 2 raised to the power of 2.6:

22.6 ≈ 6.30957

Multiply this by the initial population:

2900 bacteria * 6.30957 ≈ 18,297.753

Finally, we round the result to the nearest whole number:

≈ 18,298 bacteria

Therefore, after 13 hours, the population of bacteria in the culture is approximately 18,298.