Suppose that bacteria growth is modelled by the DE

Question

Suppose that the number of bacteria is observed to double after 4 days, and the estimated carrying capacity is

19 times the initial population. What is the estimated population, as a multiple of the initial population, after 16 days?

(For example, an answer of 3.5 would indicate a population 3.5 times the initial population).

Give the answer accurately to 2 decimal places

One of the tutors has answer P(16) = a₀(2)^16/4

but I don't really understand what he is doing

Answer 1

a₀ is the initial population.(pick a number, say 5, as the question doesn't provide a figure and they only want a multiple as the answer). The 2 represents the fact that the number of bacteria double over each of the 4-day periods.. The exponent of 16/4 shows the number of "cycles" in the 16-day period over which the bacteria are assumed to be multiplying - in this case there are four 4-day cycles in the 16-day period specified in the question.

So your equation might be P(16) = 5•2⁴. The answer would be 80, so your multiple would be 80/5, or 16. You'll see that the multiple is the 2⁴ part of the equation.