For this case we have an equation of the form:
y = A (b) ^ t
Where,
A: initial amount
b: decrease rate
t: time
Substituting values:
y = 750 (0.5) ^ ((1/15) * t)
The number of days to reach 68 mg is:
68 = 750 (0.5) ^ ((1/15) * t)
Clearing t:
(0.5) ^ ((1/15) * t) = (68/750)
log0.5 ((0.5) ^ ((1/15) * t)) = log0.5 (68/750)
(1/15) * t = log0.5 (68/750)
t = 15 * log0.5 (68/750)
t = 51.94
Rounding:
t = 52 days
Answer:
D. ≈ 52 days
