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daser333 [38]
3 years ago
11

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 th

e 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?
Mathematics
1 answer:
Hatshy [7]3 years ago
6 0
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.
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