Question 452493: an element decays in such a way that every 50 years the amount of the element of the element has decreased by 15% in the year 1900,120mg of element was present.
a)what is amount in 2000
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! an element decays in such a way that every 50 years the amount of the element of the element has decreased by 15% in the year 1900,120mg of element was present.
a)what is amount in 2000
.
A = Pe^(rt)
where
A is amount after time t
P is the initial amount
r is the rate of growth/decline
t is time
.
first, we determine r...
Let x = initial amount
then
from: "an element decays in such a way that every 50 years the amount of the element of the element has decreased by 15%"
x - .15x = xe^(50r)
x(1 - .15) = xe^(50r)
(1 - .15) = e^(50r)
.85 = e^(50r)
ln(.85) = 50r
ln(.85)/50 = r
-0.0033 = r
.
Our formula then is:
A = Pe^(-0.0033t)
.
Now, we can answer the question:
in the year 1900,120mg of element was present.
a)what is amount in 2000
t = 2000-1900 = 100
A = 120e^(-0.0033*100)
A = 120e^(-0.33)
A = 86.7 mg
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