working with logarithms

Question

Rats are placed in a large glass container with food. Suppose that the rat population after t days is given by p(t)= 150/(1+7.5e^-.28t) How long does it take for the population to reach 800?

Answer 1

Based on the information the question provided, we know that p(t) is 800 and that we are looking for t.  So if you plug into your equation, you should be able to arrange and combine like terms in order to get e^.28t by itself.  From there, keep in mind that ln(e^x)=x.  So if you take the natural log of both sides of the equation, you will be able to get t out of the exponent position and simply divide both sides by 0.28 to find your answer.

 

Good Luck!