The population P of bacteria in an experiment grows according to the equation dP/dt=kP, where k is a constant and t is measured in hours. If the population of bacteria doubles every 24 hours, what is the value of k? I was given this problem and I'm not sure what to do with it. I know the formula for this kind of equation is ce^(kx). But, how do you plug in the values given?

sponsorjewk

sponsorjewk

Open question

2022-09-03

The population P of bacteria in an experiment grows according to the equation d P d t = k P, where k is a constant and t is measured in hours. If the population of bacteria doubles every 24 hours, what is the value of k?
I was given this problem and I'm not sure what to do with it. I know the formula for this kind of equation is c e k x . But, how do you plug in the values given?

Answer & Explanation

Kaeden Bishop

Kaeden Bishop

Beginner2022-09-04Added 15 answers

So you know P = c e k t . The population doubles in 24 hours, or 2 P = c e k ( t + 24 ) . Now can you find k by dividing the two equations?
As a side note, you might want to know how that formula was obtained.
d P d t = k P d P P = k   d t
Now integrate both sides,
P ( t = 0 ) P ( t = t ) d P P = k t = 0 t = t d t
giving you P ( t ) = P ( 0 ) e k t

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?