High School

A culture of bacteria has an initial population of 400 bacteria and doubles every 2 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 :

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.

Other Questions