Answer:
75 days
Step-by-step explanation:
The multiplier each day is ...
(1/2)^(t/15)
Then we want to find t such that ...
5 = 160·(1/2)^(t/15) . . . . . . 5 mg are left after t days
5/160 = (1/2)^(t/15) . . . . . . divide by 160
1/32 = (1/2)^5 = (1/2)^(t/15) . . . . rewrite the left side
Equating exponents (equivalent to taking logs), we get ...
5 = t/15
5·15 = 75 = t . . . . . multiply by 15 to find t
After 75 days, there will be 5 mg left.
