A typical cup of coffee contains about 100 mg of caffeine and every hour approximately 16% ofthe amount of caffeine inthe body is metabolized and eliminated. a)Let C represent the amount of caffeine in the body in mg and f represent the number of hours since a cup of coffee was consumed. Write C as a function of r.
b) How much caf[eine is in the body after 5 hours?

a)

And for this case we can rewrite the model like this:

If we integrate both sides we got:

If we use exponentials for both sides we got:

For this case and r = -0.16

So then our model would be given by:

Where t represent the number of hours

b)

Step-by-step explanation:

Part a

For this case we can assume the proportional model given by:

And for this case we can rewrite the model like this:

If we integrate both sides we got:

If we use exponentials for both sides we got:

For this case and r = -0.16

So then our model would be given by:

Where t represent the number of hours

Part b

For this case we can replace the value t=5 into the model and we got:

5.25 ounces

step-by-step explanation:

divided 3/4 and 6

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1