The halflife of radium226 is 1600 years Suppose we have a 26

The half-life of radium-226 is 1600 years. Suppose we have a 26-mg sample.

(a) Find a function m(t) = m02t/h that models the mass remaining after t years. m(t) = _____

(b) Find a function m(t) = m0ert that models the mass remaining after t years. (Round your r value to six decimal places.) m(t) = _____

(c) How much of the sample will remain after 2500 years? (Round your answer to one decimal place.) _____mg

(d) After how many years will only 17 mg of the sample remain? (Round your answer to one decimal place.) _____yr

Solution

a) half life = 1600

decay constant = 0.693/1600 = 0.000433125

a) equtaion not clearly stated in question

b) m(t) = 26e^-0.000433125t

c) t = 2500 yrs

m(2500) = 26e^(-0.000433125*2500) = 8.80 mg

c) m(t) = 17mg solve fort

17 = 26e^(-0.000433125t)

ln(17/25)/-0.000433125 = t