Question: The # of bacteria grows exponentially @ 1% per hr. Assuming 10,000 bacteria are present initially...

Question

The # of bacteria grows exponentially @ 1% per hr. Assuming 10,000 bacteria are present initially, find:

a) the # of bacteria present at any time T.
b) the # of bacteria present after 5 hrs
c) the time req. for # bacteria to reach 45,000?

Please help, and please explain! This is the first question in my homework set and I just want to make sure I'm doing it the right way.

Answer 1

A = Pe^(rt), where A is the current number of bacteria at any time t, P is the initial number of bacteria, e is a mathematical constant, r is the rate at which the bacteria grow, and time is t.

a) plug in stuff
b) plug in stuff again, this time not leaving t as a variable
c) set the equation equal to 45,000, and solve for r, which is usually the more annoying part for me. Remember that if a=e^x, ln(a) = x.