Answer
a) $0.125\thinspace g$
b) $m=2(\frac{1}{2})^{\frac{1}{15}t}$
c) $0.024\thinspace g$
d) $114.66\thinspace hours$
Work Step by Step
a) We start with 2 grams after 0 hours.
After 15 hours, we have 1 gram.
After 30 hours, we have 0.5 grams.
After 45 hours, we have 0.25 grams.
After 60 hours, we have 0.125 grams.
b) We start with 2 grams and halve it every 15 hours, so the equation is $m=2(\frac{1}{2})^{\frac{t}{15}}$.
c) 4 days = 96 hours. Plug this into $t$ in part (b) to get $\approx 0.024\thinspace grams$.
d) Graph the equation in part (b) and $y=0.01$. Find the point where they intersect, which is $(114.66, 0.01)$. The answer is 114.66 hours.
