To determine the expression that represents the mass of sodium remaining after \( h \) half-lives, we can use the concept of half-life.
The mass remaining after \( h \) half-lives can be calculated using the formula:
\[ S = S_0 \left(0.5\right)^h \]
where:
- \( S_0 \) is the initial mass,
- \( h \) is the number of half-lives,
- \( S \) is the remaining mass after \( h \) half-lives.
If we assume the initial mass \( S_0 \) is 800 (which seems to be suggested by the options provided), the formula becomes:
\[ S = 800 \left(0.5\right)^h \]
Now let's check the options:
- \( S = 0.5(800)h \) - This is not correct as it does not represent the exponential decay.
- \( S = 800(0.5)^h \) - This matches our derived formula. This is the correct expression.
- \( S = 8000.5h \) - This is not correct as it also does not represent the exponential decay.
- \( S = 800h + 0.5 \) - This is not correct as it is a linear equation, not an exponential decay.
Thus, the correct expression that represents the mass of sodium remaining after \( h \) half-lives is:
\( S = 800(0.5)^h \).
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