A test tube is inoculated with 1 × 103 cells of a bacterial strain that has a generation time of 30 minutes.The carrying capacity of the test tube for this strain is 6 × 109 cells.What will the bacterial population be after 90 minutes of culturing?

Question

Quizplus · Accepted Answer

The formula to calculate the bacterial population is Nt = N0 x 2^(t/g), where Nt is the final population size, N0 is the initial population size, t is the time in minutes, and g is the generation time in minutes.

In this case, N0 = 1 × 10^3, t = 90 minutes and g = 30 minutes. Therefore:

Nt = 1 × 10^3 x 2^(90/30) = 1 × 10^3 x 2^3 = 8 × 10^3

However, since the carrying capacity of the test tube is 6 × 10^9 cells and the final population size exceeds this capacity, we have to use the logistic growth equation:

Nt = K / (1 + ((K - N0)/N0) x e^(-rt))

where K is the carrying capacity, N0 is the initial population size, and r is the growth rate.

To solve for r, we can use the formula:

r = (ln(Nt/N0)) / t

Plugging in the values, we get:

r = (ln(6 × 10^9/1 × 10^3)) / 90 = 0.208

Now we can solve for Nt:

Nt = 6 × 10^9 / (1 + ((6 × 10^9 - 1 × 10^3)/1 × 10^3) x e^(-0.208 x 90)) = 8 × 10^13

Therefore, the bacterial population after 90 minutes of culturing is 8 × 10^13, which is closest to answer choice D.

A Test Tube Is Inoculated with 1 × 103 Cells