A 12-gram sample of strontium-90 will radioactively decay to half the original quantity in approximately 29 years, and can be modeled by the following function.
$$ S(t)=12(0.5)^{\frac{t}{29}} $$
Which of the following is the best interpretation of the number 0.5 in the function?
The first choice (initial number of grams of strontium-90) refers to the number 12.
The second choice would need to
be calculated by evaluating \( S(0.5)\).
The 0.5 represents the multiplier of an exponential equation. In other words, for every \(\frac{t}{29}\) years, the initial value (12) would be multiplied by 0.5.
The
last choice sounds similar to the correct one, but it would need to mention decay after 29 years, not 12. Additionally, the number would have to be 50, to represent 50%, rather than 0.5.