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Sagot :
Answer:
The equation is [tex]A(t) = 0.52*(0.9885)^{(t)}[/tex].
0.4713 grams would remain in the tumor after 8.5 days.
Step-by-step explanation:
Exponential equation of decay:
The exponential equation for the amount of a substance that decays, after t days, is given by:
[tex]A(t) = A(0)*(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
A tumor is injected with 0.52 grams of Iodine-125.
This means that [tex]A(0) = 0.52[/tex]
After 1 day, the amount of Iodine-125 has decreased by 1.15%.
This means that [tex]r = 0.0115[/tex]
So
[tex]A(t) = A(0)*(1-r)^t[/tex]
[tex]A(t) = 0.52*(1-0.0115)^t[/tex]
[tex]A(t) = 0.52*(0.9885)^t[/tex]
Then use the formula for A(t) to find the amount of Iodine-125 that would remain in the tumor after 8.5 days.
This is A(8.5).
[tex]A(t) = 0.52*(0.9885)^t[/tex]
[tex]A(8.5) = 0.52*(0.9885)^{8.5} = 0.4713[/tex]
0.4713 grams would remain in the tumor after 8.5 days.
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