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:

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