Question

Forty grams of Iodine 131, a radioactive material, decays according to the equation A(t)=40e^(-0.087t) (t is in days and A is the amount present at time t)

a. How much iodine 131 is remaining after 5 days?


b. When will 10 grams of iodine 131 be left?

Answer 1

a.) After 5 days t=5 so:


`a(5) = 40 {e}^( - 0.087(5)) = 25.89g`
b.) Since we want to know how much time 40 grams will decay to 10 grams we will let A(t)=10 so:


`10 = 40 {e}^( - 0.087(t)) \\ \\ (10)/(40) = {e}^( - 0.087(t)) \\ \\ ln( (1)/(4) ) = - 0.087t \\ \\ ( ln( (1)/(4) ) )/( - 0.087) = t \\ \\ t = 15.93`
10 grams will be left after 15.93 days.