Question

If caffeine reduces by about 10% per hour, how many hours h does it take for the amount of caffeine in a body to

reduce by half (round up to the next hour)?

Answer 1

7 hours

Explanation:

Since, the final amount of caffeine formula would be,

`A=P(1-r)^t`

Where,

P = Initial value,

r = rate per period,

t = number of periods,

Here, r = 10% = 0.10, t = h, A =
`(P)/(2)`

`(P)/(2)=P(1-0.10)^h`

`(1)/(2)=(0.90)^h`

Taking log both sides,

`log 0.5 = log 0.90^h`

`log 0.5 = h log 0.90`

`\implies h = (log 0.5)/(log 0.9)=6.57881347896\approx 7`

Hence, after 7 hours the amount of caffeine in a body to reduce by half.