Question

Consider a population p of field mice that grows at a rate proportional to the current population, so that dp dt = rp. (note: remember that, as in the text, t is measured in months, not days. one month is 30 days.) (a) find the rate constant r if the pop

Answer 1

∫ (1/p) dp = ∫ r dt => lnp = rt + C => p = e^(rt + C) = Ae^rt (a) so, in 30 days, t = 1 => p/A = 2 = e^r i.e. r = ln2 = 0.693 (b) after N days t = N/30 => 2 = e^(rN/30) => rN/30 = ln2 i.e. r = (30ln2)/N