Question

A biologist prepares a culture. After 1 day of growth, the biologist counts 1000 cells. After 2 days of growth, he counts 3000. Assuming a Malthusian model, what is the reproduction rate and how many cells were present initially

Answer 1

Answer: The equation of the Malthusian model is P (t) = Cert . Apply the cell

counts to solve for r and C. P (1) = 1000, so Cer = 1000, i.e. r = ln(1000/C).

Also, P (2) = 3000, so Ce2r = 3000, i.e. r = 1

2 ln(3000/C). Setting these equal

and solving, one obtains C = 1000/3. Substituting C into r = ln(1000/C) gives

that r = ln 3.