Bacterial Growth, anyone? The rate of growth of bacteria is proportional to the amount present. If initially there are 100 bacteria and 5 minutes later there are 150 bacteria, how many bacteria will be present after 1 hr?

Question

anonymous · Answer

Growth is given by: $$P(t) = P_{0} e^{kt} $$t in minutes and k is a positive constant. From the first condition, we solve for Po (Po = 100). For t = 5, we solve for k. Then, use t = 60 :-)

anonymous · Answer

I got 12974, but check my arithmetic.

anonymous · Answer

thats what i got

anonymous · Answer

thanks

anonymous · Answer

No problem. Just to be more general: $$ \frac{dP}{dt} = kP $$Where k is a positive constant for growth, and negative for decay. Solve the DE, and you will get a solution like the one above. That's way P(t) is given by that.

anonymous · Answer

ummm i got 12975?

anonymous · Answer

That's okay. It's the rounding errors. We want integers for population (population is not continuous) and it's an exponential growth, every rounding we do for k changes the end result by a lot.

anonymous · Answer

rounding error*. Can't pluralize today...

anonymous · Answer

lol

anonymous · Answer

thanks :)