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

Answer 1

Answer:

7 hours

Step-by-step 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 = $\frac{P}{2}$

$\frac{P}{2}=P(1-0.10)^h$

$\frac{1}{2}=(0.90)^h$

Taking log both sides,

$log 0.5 = log 0.90^h$

$log 0.5 = h log 0.90$

$\implies h = \frac{log 0.5}{log 0.9}=6.57881347896\approx 7$

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