To model the decay of a radioactive substance, we can use the exponential decay formula:
\[ f(t) = f_0 \cdot e^{-kt} \]
where:
- \( f(t) \) is the amount of substance at time \( t \),
- \( f_0 \) is the initial amount of the substance,
- \( k \) is the decay constant, and
- \( t \) is time in years.
In this case, the initial amount \( f_0 \) is 600 grams and the substance decays at a rate of 6% each year. This means that after one year, 94% of the substance remains (100% - 6% = 94%).
Thus, the decay can be modeled with the following formula:
\[ f(t) = 600 \cdot (0.94)^t \]
Now, let's check the given options to see which one matches this model.
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Option #1: \( f(x)=600(0.06)x \) - This represents growth and does not model decay.
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Option #2: \( f(x)=600(1.06)x \) - This also represents growth (an increase of 6%).
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Option #3: \( f(x)=600(0.6)x \) - This suggests a constant decay to 60% of the original amount, which is not correct.
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Option #4: \( f(x)=600(0.94)x \) - This is the correct model of decay, as it indicates that 94% of the substance remains each year.
Therefore, the correct option that models the decay of the substance is:
Option #4: f(x)=600(0.94)x