Question

I would really appreciate it if someone could take a look at this calculus problem with exponential growth and let me know if it is correct. I am not so confident in my answer to Part A. If Part A is wrong, then everything else is wrong!

Answer 1

The answer appears to be correct all around.

Of course, e^(ln(0.6)) = 0.6, so you really have 3500 -0.6^(t/5). This exponential term will vanish for large t, so the limit will be 3500.

You can also come to that conclusion from the original problem statement. As the population approaches 3500, the rate of change of population approaches zero, since it is proportional to the difference from 3500.