1. ## Doubling time

Mike raises mink, which reproduce exponentially. He currently has 50 mink in his garage, where a month ago he had only 40.
How long does it take the number of mink to double?

ok so the rate is $\displaystyle (50-40)/40 = 0.25$

$\displaystyle 100 = 50e^{0.25T}$

$\displaystyle T=4ln2$ <---- is this 4ln2 month or 4ln2 year?

2. Originally Posted by cammywhite
Mike raises mink, which reproduce exponentially. He currently has 50 mink in his garage, where a month ago he had only 40.
How long does it take the number of mink to double?

ok so the rate is $\displaystyle (50-40)/40 = 0.25$

$\displaystyle 100 = 50e^{0.25T}$

$\displaystyle T=4ln2$ <---- is this 4ln2 month or 4ln2 year?
How do you figure?

We are told that they reproduce exponentially so the equation is of the form

$\displaystyle y=Ca^t$

we know that at t=0 y=40

$\displaystyle 40=Ca^{0} \iff 40 = C$

$\displaystyle y=40a^{t}$ then in one month t=1 y=50

$\displaystyle 50=40a^{1} \iff a=\frac{5}{4}$

So the equation is

$\displaystyle y=40\left( \frac{5}{4}\right)^t$

we want to know when y=80

$\displaystyle 80=40\left( \frac{5}{4}\right)^{t}$

Now all we need to do is solve this equation for t.