composite function

Question

The effect of caffeine, c in milligrams, on a person's heart rate, r, in beats per minute can be modeled by the function r(c)=80+0.03c. The dissipation of caffeine from the bloodstream over time since ingestion, t, in hours can be modeled by the function c(t)=-28t+300. 

 

Determine the amount of caffeine in a person's bloodstream 3 hours after ingestion.

 

Determine a person's heart rate 2 hours after ingesting caffeine. Show your Work.

Answer 1

This is a fairly simple word problem requiring you to recognize what the variables are and plug them in to solve.

For the first part, we can use the second equation given, plugging 3 in for t.

c(3) = -28(3) + 300
c(3) = -84 + 300
c(3) = 216

Thus, 3 hours after ingestion, a person's bloodstream contains 216 mg of caffeine.

For the second part, we will use this equation again to solve for c, then plug c into the first equation to determine heart rate.

c(2) = -28(2) + 300
c(2) = -56 +300
c(2) = 244

r(244) = 80 + 0.03(244)
r(244) = 80 + 7.32
r(244) = 87.32

So, 2 hours after ingesting coffee, a person's heart rate will be 87.32 beats per minute.