To model the decay of a radioactive substance, we typically use the formula:
\[ f(t) = f_0 \cdot (1 - r)^t \]
where:
- \( f(t) \) is the amount of substance at time \( t \),
- \( f_0 \) is the initial amount,
- \( r \) is the decay rate (as a decimal),
- \( t \) is the time in years.
Given that the decay rate is 6%, we can express this as \( r = 0.06 \). The initial amount is 600 grams.
Therefore, the function for this decay would be:
\[ f(t) = 600 \cdot (1 - 0.06)^t \] \[ f(t) = 600 \cdot (0.94)^t \]
Now, let's look at the options provided:
- Option #1: \( f(x) = 600 (0.06)^x \) (This is incorrect as this represents a growth rather than decay.)
- Option #2: \( f(x) = 600(1.06)^x \) (This is incorrect as this also represents growth rather than decay.)
- Option #3: \( f(x) = 600(0.6)^x \) (This is incorrect as this does not represent the given decay rate.)
- Option #4: \( f(x) = 600(0.94)^x \) (This is correct as it represents the 6% decay.)
Thus, the option that correctly models the problem is Option #4: \( f(x) = 600(0.94)^x \).