Compartment Model

[heyheyhey701]

Suppose that strontium-90 is being introduced at an absolute rate of .5 grams per day, and is removed at a relative rate lambda, which can be expressed in terms of the half life of st90, which is 30 years. If s(t) denotes the amount in grams of st90 remaining after t years, then compute the amount of st90 in the environment in the long run. that is, find s(infinity) = lim as t approaches infinity of s(t)

 

[tkhunny]

Go for it. Let's see your model.

Current Amount = Initial Amount + Amount Introduced since Inception - Amount Decayed since inseption

In this case, the "Rate In" is constant. That makes it easier. The "Rate Out" is proportional to the Initial Amount.

ds/dt = s(t)*(RateOut) + RateIn

Are we getting anywhere?