Half Life Question

[rbirkenholz]

I have a situation where there is a mass flow rate into a system of 2.5 g/hr. The substance has a half life of 29 hours. The period of study is 2000 hours. I need to know how much of the substance remains after 2000 hours.

I THINK that the mass at any given time is:

INTEGRAL OF( 2.5 * t * e^[-0.693 * t / 29]) from 0 to 2000

I get an answer of 4377.94 grams. Does this seem correct? Have I applied the integration correctly?

 

[morson]

Have you set up the required differential equation?

 

[rbirkenholz]

No, I haven't. This can't be done with integral calculus?

 

[Deleted member 4993]

You'll use integral calculus to solve the problem.

However, you need to set the DE from the physics of the problem - so that you get the correct integral.

Loss of material = (k * P) dt

Incoming material = 2.5 dt

So material accumulating = [2.5 - (k*P)] dt

Then you integrate to get the proper value.