decay prob: find limiting amt of radium over time

[mooshoorama]

Radium-226 has a half life of 1620 years. If 10mg of this material are initially present in a container and additional radium-226 is added to the container at a constant rate of .002 mg/year, find the amount of the material in the container at any time and the time period during which this material is reduced to three-fourths of its original amount. Then find the limiting amount as t approaches positive infinity.

I've figured out that the K in this problem is:

. . .K = 4.28x10^-4.

The answer that my teacher gave is:

. . .Q(t) = 4.673 + 5.327e^(-4.28x10^-4)

But I can't figure out how the teacher got that answer. Ideas? Thank you!

 

[galactus]

This is similar to the brine tank problems. Remember those?.

Since it's radium, I'll use R.

dR/dt=rate added per year - rate decayed per year.

Try setting up your DE. Find the integrating factor. Use the I.C. to find C.