Question

1. A cup of coffee contains approximately 100 milligrams of caffeine. After you drink a cup of coffee, the amount of caffeine in your body is reduced by 13% each hour.

a) Write an equation to represent the amount of caffeine N, in milligrams, In hours after you drink coffee

b) Use your equation to estimate the amount of caffeine left in your body 10 hours later​

Answer 1

a. 100-13x.

b. 100 - 13 (10)= -30. Since you cannot have a negative value of the quantity of a substance inside an body, when the function gives 0 or a negative value, it means that caffeine is not present in the body anymore. Therefore, after 10 hours there isn't any amount caffeine in your body.

Explanation:

We are gonna represent time with the variable x, so at the start of the experiment, when when you drink the coffee, x= 0. Now, the amount of caffeine in the body (in milligrams) will be the y variable.

At the time you drink the coffee, the amount of caffeine in the body is 100 milligrams, therefore, a point is created (0(x),100(y)).

In order to create a second point, be aware that each hour the amount of caffeine is reduced by 13%, meaning that on hour 1 you have another point given by (1(x), (100-(100*0.13))(y))= (1(x), (100-(13))(y))=(1(x), 87)(y)).

Now, take the 2 points and find the slope using the following formula:

`m=(y2-y1)/(x2-x1) =(87-100)/(1-0) =(-13)/(1)=-13`

Now, with one point the the value of the slope, let's generate a formula for this data:

`y-y1=m(x-x1)\\y-87=-13(x-1)\\y-87=-13x+13\\y=-13x+13+87\\y=-13x+100\\y=100-13x`

a. 100-13x.

b. 100 - 13 (10)= -30. Since you cannot have a negative value of the quantity of a substance inside a body, when the function give 0 or a negative value, it means that caffeine is not present in the body anymore. Therefore, after 10 hours there isn't any amount of caffeine in your body.