Question 252075
All exponential models are of the form {{{ Y = Ae^kt}}} where A is "initial value", k is "growth rate", t is time units, and Y is "ending value".

So, initially there were 200 bacteria. Since we triple, Y = 3*200 = 600. Now for time; t = 2. We don't know the growth rate, k. This is step 1 in these kind of problems.

Our formula now becomes first {{{ 600 = 200e^(2k)}}} then {{{3 = e^2k}}} and taking a natural log (LN) of both sides we get ln(3) = 2k, and finally solving for k, we get k = ln(3)/2.

Knowing k, we can now find how many there are after 5 hours.

Y = 200*e^(5*ln(3)/2) becomes Y = 3118 rounded to the nearest bacteria.