SOLUTION: Use the formula N=Ie^kt, where N is the number of items of the initial population "I", at the time "t", and "k" is the growth constant equal to the percent of growth per unit of ti

Question 1131793: Use the formula N=Ie^kt, where N is the number of items of the initial population "I", at the time "t", and "k" is the growth constant equal to the percent of growth per unit of time. A certain radioactive isotope has a half-life of approximately 1750 years. How many years would be required for a given amount of this isotope to decay to 25% of that amount?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This would be 2 half-lives or 3500 years
N=Ie^(1750k)
divide by I and N/I=1/4
1/2=e^(1750k)
ln of both sides
-ln2=1750k
k=-ln2/1750=-0.000396
N/I=0.25=e^(0.000396*t)
ln(0.25)=0.000396t
-ln4/-0.000396=t=3500.74 years, but 3500 is exact.

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