SOLUTION: How long will it take any quantity of iodine 131 to decay to 25% of its initial amount, knowing that it decays according to the function defined by A(t)=A

SOLUTION: How long will it take any quantity of iodine 131 to decay to 25% of its initial amount, knowing that it decays according to the function defined by A(t)=A_0 e^(-.087t), where t i

Question 599866: How long will it take any quantity of iodine 131 to decay to 25% of its initial amount, knowing that it decays according to the function defined by A(t)=A_0 e^(-.087t), where t is time in days?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
How long will it take any quantity of iodine 131 to decay to 25% of its initial amount, knowing that it decays according to the function defined by A(t)=A_0 e^(-.087t), where t is time in days?
.
Let x = initial amount
then plugging in to the given equation we get:
.25x = xe^(-.087t)
dividing both sides by x:
.25 = e^(-.087t)
take ln of both sides:
ln(.25) = -.087t
ln(.25)/(-.087) = t
15.93 days = t

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