SOLUTION: Suppose the half-life of a certain radioactive isotope is 11 minutes. If 21 per cent of the initial quantity is remaining, how many minutes old is the isotope? Answer: t =

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Suppose the half-life of a certain radioactive isotope is 11 minutes. If 21 per cent of the initial quantity is remaining, how many minutes old is the isotope? Answer: t =       Log On


   

Question 882113: Suppose the half-life of a certain radioactive isotope is 11 minutes. If 21 per cent of the initial quantity is remaining, how many minutes old is the isotope?

Answer: t = ?
Thanks so much!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
A=Ie%5E%28-kt%29 Exponential Decay Equation.
A = final amount
I = initial amount
t time in minutes
k = constant for the specific decaying material

You know these values:
A=21
I=100
-
The 11 minutes half life information allows you to find k.



USE HALF LIFE TO FIND k.
ln%28A%29=ln%28I%29%2B%28-kt%29ln%28e%29
ln%28A%29-ln%28I%29=-kt%2A1
kt=ln%28I%29-ln%28A%29------you will use this again later.
k=%28ln%28I%29-ln%28A%29%29%2Ft
highlight_green%28k=%281%2Ft%29ln%28I%2FA%29%29---as a formula.
The half-life data meant I=1, A=1/2, t=11.
k=%281%2F11%29ln%281%2F%281%2F2%29%29=%281%2F11%29ln%282%29
k=0.06301
-
Decay Equation Model, highlight_green%28A=Ie%5E%28-0.06301t%29%29


USE DECAY EQUATION TO ANSWER t.
Start from kt=ln%28I%29-ln%28A%29;
highlight%28t=%281%2Fk%29ln%28I%2FA%29%29;
Substitute the known values for k, I, and A; and compute t.
A=21, I=100, k=0.06301.