Respuesta :
The initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.
How to determine the amount
From the information given, we have the function to be;
a(t)=2400(1/2)^t/14
Where
- a(t) is the final amount
- t represents time
- 'I4' is the half life of the radioactive substance, Uranium - 240
To determine the initial amount, we have that t = 0
Substitute into the function, we have
[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{0}{14}[/tex]
[tex]A (t) = 2400[/tex] × [tex]\frac{1}{2} ^0[/tex]
[tex]A (t) = 2400[/tex]
The initial amount is 2400 grams
For the amount remaining after 40 years, t = 40 years
A(t)=2400(1/2)^t/14
Substitute into the function, we have
[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{40}{14}[/tex]
[tex]A(t) = 2400[/tex] × [tex](0. 5) ^2^.^8^5^7[/tex]
[tex]A(t) = 2400[/tex] × [tex]0. 1380[/tex]
A(t) = 331. 26
A(t) = 331 grams in the nearest gram
Thus, the initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.
Learn more about half life here:
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