Population Growth Problem

Question

Suppose that the number of bacteria is observed to double after 9 days, and the estimated carrying capacity is 7 times the initial population. What is the estimated population, as a multiple of the initial population, after 19 days?

Answer 1

Since you give a carrying capacity, I assume you are dealing with a logistic equation problem rather than just exponential population growth.

Assuming the doubling time is clear of the limits of carrying size (we can check later)

2P₀ = P₀e^{k(9 days)} so k = ln(2)/9 = .077016 days^-1

The logistic equation solution is P = P₀Ke^kt/((K-P₀)+P₀e^kt)

Divide through by P₀: P/P₀ = (K/P₀)e^kt/((K/P₀-1)+e^kt)

Substitute into this equation t = 19 days, k = .077016, and K/P₀=7

Please consider a tutor. Take care.

(You can try the equation for 7 days and see how close to 2 P/P₀ is in order to check the exponential growth assumption).