11 If \( f(t)=50(.5)^{\frac{t}{5715}} \) represents a mass, in grams, of carbon-14 remaining after \( t \) years, which statement \( (\mathrm{s}) \) must be true?
I. The mass of the carbon-14 is decreasing by half each year.
II. The mass of the original sample is \( 50 \mathrm{~g} \).
(1) I, only
(3) I and II
(2) II, only
(4) neither I nor II

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Answer

Answer: (2) II, only

Steps

Step 1 ：\( f(t)=50(.5)^{\frac{t}{5715}} \): - \( t=0 \) years, \( f(0)=50 \) grams

Step 2 ：For \( t=5715 \) years, \( f(5715)=50(.5)^{\frac{5715}{5715}}=50(.5) = 25\) grams

Step 3 ：Answer: (2) II, only