Answer:
7 hours
Step-by-step explanation:
Since, the final amount of caffeine formula would be,
[tex]A=P(1-r)^t[/tex]
Where,
P = Initial value,
r = rate per period,
t = number of periods,
Here, r = 10% = 0.10, t = h, A = [tex]\frac{P}{2}[/tex]
[tex]\frac{P}{2}=P(1-0.10)^h[/tex]
[tex]\frac{1}{2}=(0.90)^h[/tex]
Taking log both sides,
[tex]log 0.5 = log 0.90^h[/tex]
[tex]log 0.5 = h log 0.90[/tex]
[tex]\implies h = \frac{log 0.5}{log 0.9}=6.57881347896\approx 7[/tex]
Hence, after 7 hours the amount of caffeine in a body to reduce by half.
