Finding mass of "t" number of years from given half life.

Question

The half-life of cesium-137 is 30 years. Suppose we have a 100-mg sample. Find the mass that remains after t years. How much of the sample remains after 200 years?

Answer 1

Your initial mass is 100mg. The half life indicates that after 30 years, the sample size halves, which is the same as multiplying by 1/2.

So your equation for mass remaining is x=100*(1/2)^t/30. Since you only multiply by 1/2 every 30 years, you want to divide the t in the exponent by 30, otherwise you would effectively be halving the sample size every year.

To identify sample size after 200 years, simply substitute the 200 for t as shown below:

x=100*(1/2)^200/30=0.98mg.