radium decomposes at a rate propotional to the amount present.if p percent of the original amount disappears in l years how much will remain at the end of 2l years?
Let m be the percentage mass of radium present at time t.
Let be the mass present at time .
where k is a real constant (k is actually negative since this is "exponential decay". You can write k=-b or something to show that you know it is negative. I just left it because it doesn't change the overall answer at the end.)
Integrating gives:
where
using the intial conditions:
when t=I years:
At t=2I years:
and I think we're done! =D
P.S: I did change notation. I used m instead of p. If you like you can work it through again with m=p or just write this at the end.
Hello, padmini priya!
Let = quantity of radium at timeRadium decomposes at a rate propotional to the amount present.
If percent of the original amount disappears in years.
how much will remain at the end of years?
We have: .
Integrate: .
When (initial amount)
We have: .
The function (so far) is: .
When
So we have: .
. . Hence: .
The function is: .
When
We have: .
Therefore: .
. .