Exponential Functions Equation

You could also use geometric series, there's really no need to integrate here.

Say we have n black moths, then the population of moths will be


And the population of grey moths will be


Solving for t:


And the rest is pretty straightforward.

Noah

Actually Noah... this brings up an interesting point... Should we NOT count this as continuous growth? I thought we should because this is a population growth problem, thus I used the continuous growth model. But you used the non continuous exponential growth model that is usually used for things like interest which is applied only once in a given period:



(Granted, you used geometric series... but that gives you the non continuous result)

So we use Integrate instead of Log? Ok. Thanks!

Edit: It seems there is two ways to solve it? I'll just wait until tomorrow. The thanks still stands.

I have another question: Is this assuming that they start with the same value? As in equal amounts of both? Because the question says that it starts as twice as many grey moths than blacks.

And we assumed that they started with the values you told us about.

That's why we have 2a and a in the equations (in my case), and 2n and n in Noah's equation.

Also... when you solve for t... you get t in terms of a natural log. So natural logs WILL be involved in the answer.