 #1
fogvajarash
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Homework Statement
A certain nuclear plant produces radioactive waste in the form of strontium90 at the constant rate of 500kg. The waste decays exponentially with a halflife of 28 years. How much of this radioactive waste from the nuclear plant will be present after the following increments of time? Assume that initially 600kg of strontium90 is in the nuclear plant.
a. N years
b. 140 years
c. To perpetuity
Homework Equations

The Attempt at a Solution
I found that the "rate in" was 500kg/year, and I'm not sure about the "rate out" (rate of depletion of the sample).
We are given that the sample decays exponentially, so we should have that y(t) = yo e^{0.02475t}. We can assume that yo is just y (the radioactive sample that is decaying). Then, the rate of depletion would be (I doubt that this is true):
y'(t) = 0.2475ye^{0.02475t}
This is because this is the rate of change of the sample. Then, i set up my differential equation to be the following (k is just the constant k = (ln2)/(half life)):
dm/dt = 500  kme^{kt}
I rearranged the terms into the form dm/dt  P(x)y = f(t), i came up that the integrating factor was actually ee^(kt)), but this is not true (while differentiating the function I realized that it it was a completely new expression that was different to the one shown).
How can I proceed from this information or have i made a wrong setup to the exercise?
Thank you.