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 = (b) find r if the population doubles in n days. r = ?

a)

b)

Step-by-step explanation:

For this case we assume the followin differential equation:

Where is is the consttant growth/decay rate , p represent the population and the the time.

For this case we can rewrite this expression like this:

And now we can apply integrals on both sides like this:

If we apply exponential on both sides we got:

And from the previous equation represent the initial population.

Part a

For this case we are assuming that the population doubles in t=210 so then we can set the following equation:

We can cancel in both sides and we got:

We can apply natural log on both sides and we got:

Part b

For this case we are assuming that the population doubles in t=N so then we can set the following equation:

We can cancel in both sides and we got:

We can apply natural log on both sides and we got:

you have 6 cupcakes