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 population doubles in 210 days. (round your answer to four decimal places.) r = 19.0279 incorrect: your answer is incorrect.

Answer 1

This is the concept of differential equations, given that
dp/dt=rp
then:
dp/p=rdt
thus:
ln p=rt+C
p=e^(rt+C)
P=Ke^(rt)
when t=210 days=7 months, p=2k
2k=k×e^(7r)
2=e^(7r)
ln2=7r
r=ln(2)/7
r=0.0990