Question

A college student ingests 300 mg of caffeine at 6:00 am. He metabolizes the caffeine at 18% per hour. About how much caffeine is still in his system by 9:00 am?

Answer 1

The correct answer is 138 mg.

Explanation:

To understand this problem we must first analyze it.

We know that the student's body metabolizes 18% of the caffeine ingested every hour.

Therefore we can solve that percentage to already have the number of metabolized caffeine per hour:

(300. 18): 100 =

5400: 100 = 54 mg

We now know that the student's body will metabolize 54 mg of caffeine per hour.

The question is much caffeine is still in his system by 9:00 am?

From 6:00 am to 9:00 am we have 3 hours of difference: 3 . 54 = 162

In three hours 162 mg of caffeine were already processed by his body, therefore, it still needs to be metabolized: 300 - 162 = 138 mg.

Answer 2

the number of caffeine still in his system by 9:00 am is 192 mg.

Explanation:

given information

the mass of initial caffein, m₁ = 300 mg

time, t = 9 - 6 = 2 hours

metabolised = 18%/hour = 0.18/h = 0.18 x 300 mg = 54 mg/h

the student metabolised the caffeine 54 mg/h. thus from 6 am to 9 am the caffeine metabolised is

metabolised in 2 hr = 2 x 54

= 108 mg

the remaining caffeine = initial caffeine - metabolised caffeine

= 300 - 108

= 192 mg