00:01
In this question, we are given that the half life of caffeine in a human body, t half, is equal to 6 .4 hours.
00:10
We are also given that a cup of coffee has about 85 milligrams of caffeine, and we are to write an equation for the amount of caffeine in a person's body after drinking a cup of coffee.
00:21
Since we are talking about the half -life here, we know that this is an exponential model, and it's a decay model, since the amount of caffeine is decreasing.
00:31
It will be in the form c is equal to c knot e to the power of minus k t is the initial amount and k is the tk constant now we know that the decay constant k is given by lean of 2 over t half so in this case we have lean of 2 over 6 .4 hours and our c knot is the initial amount which is 85 milligrams when a person has drunk a cup of coffee.
01:07
Therefore our model will be c is equal to 85 e to the power of minus lin of 2 over 6 .4 by t.
01:22
Now this can be simplified to e to the power of let's say lean 2 first lean of 2 multiply by minus t over 6 .4 and e lin of 2 gives us 2 to the power of minus t over 6 .4.
01:48
And this is our model of the decay for the amount of coffee in a person in body at t hours...