SOLUTION: A radioactive substance follows the decay equation dA/dt = kA.
If 20% of the substance disappears in 10 years, what is its half-life?
Algebra.Com
Question 1122744: A radioactive substance follows the decay equation dA/dt = kA.
If 20% of the substance disappears in 10 years, what is its half-life?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
}{dt}\ =\ kA(t))
Negative because # atoms is decreasing
}{A(t)}\ =\ -kdt)
}_{A_o}\,\frac{dA}{A}\ =\ -\int_0^t\,kdt)
Where 
is the quantity at time 
|\ -\ \ln|A_o|\ =\ -kt)
}{A_o}\|\ =\ -kt)
}{A_o}\|}}\ =\ e^{-kt})
}{A_o}\ =\ e^{-kt})
\ =\ A_oe^{-kt})
If 20% has decayed in 10 years then the ratio of the initial amount to the ending amount is 0.80. Therefore:
\ =\ \ln\(e^{-10k}\))
}{10})
So, for the half-life:
}{10}t})
Just solve for 
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
A standard measurement of the speed at which a radioactive substance decays is its half... (answered by ewatrrr)
A certain radioactive substance decays exponentially and has a half-life of 78 years.... (answered by stanbon)
in 10 years, 25% of a radioactive substance decays. What is its... (answered by ankor@dixie-net.com)
Find the half life of a radioactive substance that decays by 20% in 10... (answered by stanbon)
8. Radioactive materials like uranium follow the law of uninhibited decay, which is an... (answered by josgarithmetic)
The half-life of a radioactive substance is 1500 years.
a) What does the model look... (answered by ankor@dixie-net.com)
A radioactive substance decays from 20 pounds to 19.9 pounds in 25 years. approximate the (answered by Fombitz)
hi i got this question based on exponential methods i have tried but sadly not succeeding (answered by scott8148)
A radioactive substance is known to decay according to the continuous expo-nential model... (answered by solver91311)