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)=75+.05c. The dissipation of caffein from the bloodstream over time since ingestion, t, in hours can be modeled by the function c(t)= 345e^-.1215t. Find and simplify the composite function: r(c(t))=

Answer 1

Answer:

The composite function is $r(c(t))=75+17.25e^{-0.1215t}$.

Step-by-step explanation:

It is given that the effect of caffeine, c, in milligrams, on a person’s heart rate, r, in beats per minute can be modeled by the function

$r(c)=75+0.05c$         .... (1)

The dissipation of caffeine from the bloodstream over time since ingestion, t, in hours can be modeled by the function

$c(t)=345e^{-0.1215t}$     .... (2)

We have to find the composite function r(c(t)).

Using equation (1), we get

$r(c(t))=r(345e^{-0.1215t})$

Using equation (2), we get

$r(c(t))=75+0.05(345e^{-0.1215t})$

$r(c(t))=75+17.25e^{-0.1215t}$

Therefore the composite function is $r(c(t))=75+17.25e^{-0.1215t}$.