Consider a population p of field mice that grows at a rate proportional to the current population, so that dy/dt=rp.
a) Find the rate constant r if the population doubles in 30 days.
b) Find r if the population doubles in N days.
Consider a population p of field mice that grows at a rate proportional to the current population, so that dy/dt=rp.
a) Find the rate constant r if the population doubles in 30 days.
b) Find r if the population doubles in N days.
It should be dp/dt = rp.
Separating variables,
dp/p = rdt
lnp = rt + c
p = Ce^(rt)
a) 2C = Ce^(r*30)
r = ln(2) /30
b) 2C = Ce^(r*N)
r = ln(2) /N
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Attn: There is a quick way to get the answer for any exponential growth or decay.
C = C_{0} (2)^(r*t)
2C_{0} = C_{0} (2)^(r*N)
Solve for r,
r = ln(2)/N