The half-life of cesium-137 is 30 years. Suppose we have a 15-g sample.

Question

The half-life of cesium-137 is 30 years.

 

Suppose we have a 15-g sample.

 

Find a function m(t) = m02−t/h that models the mass remaining after t years. 

 

m(t) =


Find a function m(t) = m0e−rt that models the mass remaining after t years. (Round your r value to four decimal places.)

 

m(t) =


How much of the sample will remain after 61 years? (Round your answer to one decimal place.)

 

______g

 

After how long will only 4 g of the sample remain? (Round your answer to the nearest whole number.)

 

t =_________ yr

Answer 1

1/2 = e^-30r

r = ln.5/-30 = rate of decay = about 2.3% annually

m(t) = 15e^-.023t where m=mass after t years

after 61 years (which is slightly more than double the 30 year half life) there should be about 1/2 of 1/2 of 15 = 15/4 = about 3.75 or slightly less than 3.75

m(61) = 15e^-.023(61) = about 3.7 grams

or = about 3.688 grams

it reaches 4 grams a little less than 60 years, a little less than 2 half lives

4 = 15e^-.023t

4/15 = e^-.023t

-.023t = ln(4/15)

t = ln(4/15)/-.023 = about 57.5 years