Radioactive isotopes break down over time and the amount pre

Radioactive isotopes break down over time and the amount present in a substance decays exponentially. The half-life of a radioactive isotope is defined to be how much time it takes for the amount present m a substance to decrease by half. In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear weapons and got into the bones of people alive at the time. If the half-life of strontium-90 Is 31 years, what fraction of the strontium-90 absorbed in 1962 remained in people s bones In 2000? Fraction =

Solution

Q=Qoe^(kt) Qo=initial quantity of strontium Q= quantity of strontium at time t
1/2Qo=Qoe^(k31) because 31 is the half-life of strontium-90
0.5=e^(31k)
ln(0.5)=31k
k=[ln(0.5)]/31
k=-0.02235
now from 1962 to 2000 number of years are 38 so t=38
Q=Qo e^[38(-0.02235)]
Q=0.4277Qo so in 2000 remanined 42.77% of strontium-90