Very close, but not quite. Show me some steps.
Hmm. Turns out you can't do that. You know you've got the equation
You can just plug in the 3000 for the 2000, because, as you can see, if you put in a 0 for the t, you just get , which is correct for the second colony. You need to get another equation in order to solve for b. What are the conditions for the second colony? How can you get an equation from that condition?
Oops. I made a mistake. It should be
leading to the equation
This is a nontrivial algebraic equation to solve. The first thing to do, I think, would be to divide both sides by 1000, giving you
Any ideas from here?
A computer scientist, eh? For the computer scientist, log means base 2. For the scientist, it's base e. For the engineer, it's base 10. It doesn't really matter a whole lot which one you use, as long as your calculator can do it. I'd agree with your result, so long as you write the parentheses this way:
Now what can you do with this? (Hint: the logarithm of a product is the ... )