To model the decay of a radioactive substance that decays at a rate of 6% per year, you can use the formula for exponential decay:
\[ f(t) = A_0 e^{-kt} \]
However, for a simpler model using discrete time intervals (like years), you can use:
\[ f(t) = A_0(1 - r)^t \]
where:
- \( A_0 \) is the initial amount,
- \( r \) is the decay rate (in decimal form),
- \( t \) is the time in years.
In your case:
- The initial amount \( A_0 = 600 \) grams,
- The decay rate \( r = 0.06 \).
Thus, the model can be set up as:
\[ f(t) = 600(1 - 0.06)^t \]
\[ f(t) = 600(0.94)^t \]
Now, let's compare this to your provided options:
- \( f(x) = 600(0.06)^x \)
- \( f(x) = 600(0.40)^x \)
- \( f(x) = 600(0.6)^x \)
- \( f(x) = 600(0.94)^x \)
The correct model for the decay of the substance is:
f(x) = 600(0.94)^x