A culture of yeast grows at a rate proportional to its size. If the initial population is 2000 cells and it doubles after 3 hours, answer the following questions.

Question

A culture of yeast grows at a rate proportional to its size. If the initial population is 2000 cells and it doubles after 3 hours, answer the following questions.

1. Write an expression for the number of yeast cells after t hours.  

2. Find the number of yeast cells after 10 hours. 

3. Find the rate at which the population of yeast cells is increasing at 10 hours. Answer (in cells per hour): 

Answer 1

Because they are talking about doubling rate, it makes sense to use 2 as your base rather than e, but that is a matter of taste.

a) N = N₀* 2^t/τ where τ is the doubling time. When t = τ, the number of yeast cells will be twice as many (N = 2N₀)

b) Plug into the equation N₀ = 2000 t = 10 hrs τ = 3 hrs.

c) Find dN/dt at t = 10 hours. Here is the only reason to use base e as the derivative is easier. Remember that

d/dt(a^nt) = na^nt ln(a)

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