SOLUTION: Suppose that 5g of a radioactive substance decrease to 4g in 30 seconds . How long does it take for 3/5 of the substance to decay?

Question 688702: Suppose that 5g of a radioactive substance decrease to 4g in 30 seconds . How long does it take for 3/5 of the substance to decay?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Suppose that 5g of a radioactive substance decrease to 4g in 30 seconds .
find the half-life of the this substance
A = Ao*2^(-t/h), where
A = amt after t time
Ao = initial amt
t = time of decay
h = half-life of substance
:
5*2^(-30/h) = 4
2^(-30/h) = 4/5
2^(-30/h) = .8
ln(2) = ln(.8)
=
= -.322
h =
t ~ 93 seconds is the half life of the substance
:
How long does it take for 3/5 of the substance to decay?
3/5 decay of 5g leaves 2g remaining
5*2^(-t/93) = 2
2^(-t/93) = 2/5
2^(-t/93) = .4
=
= -1.322
t = -93 * -1.322
t ~ 123 seconds
:

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