SOLUTION: Radioactive strontium 90Sr has been deposited in a large field by acid rain. If sufficient amounts make their way through the food chain to humans, bone cancer can result. It has b

Question 236324: Radioactive strontium 90Sr has been deposited in a large field by acid rain. If sufficient amounts make their way through the food chain to humans, bone cancer can result. It has been determined that the radioactivity level in the field is 1.7 times the save level S. 90Sr decyas according to the formula
A(t)=Aoe^-0.0239t
where Ao is the amount curretly in the field and t is the time in years. How many years will it take until the field is contaminated.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Radioactive strontium 90Sr has been deposited in a large field by acid rain. If sufficient amounts make their way through the food chain to humans, bone cancer can result. It has been determined that the radioactivity level in the field is 1.7 times the save level S. 90Sr decyas according to the formula
A(t)=Aoe^-0.0239t
I think they want to know when the fields will be safe.
.
A(t)=Aoe^-0.0239t
Let x = initial amount of strontium
then
x/1.7 = A(t)
.
x/1.7 = xe^-0.0239t
1/1.7 = e^-0.0239t
ln(1/1.7) = -0.0239t
ln(1/1.7) /-0.0239 = t
22.2 years = t (years before the strontium decays to safe levels)

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