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#14251

functions

exponential

applications

hard

120 sec

The mass $M$ (in grams) of a radioactive substance $d$ days after it is produced is given by the function $M (d) = 500 (0.5)^{\frac{d}{3}}$ , where 3 is the half-life in days. Which of the following functions best models the mass $P$ (in grams) of the substance $h$ hours after it is produced?

A.

$P (h) = 500 (0.5)^{\frac{h}{3/24}}$

B.

$P (h) = 500 (\frac{0.5}{24})^{\frac{h}{3}}$

C.

$P (h) = \frac{500}{24} (0.5)^{\frac{h}{3}}$

D.

$P (h) = 500 (0.5)^{\frac{h}{72}}$