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: