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.

Question

Mathematics

Dahlia Cordova

23 August, 12:32

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.

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Santos Vang · 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