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

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

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)`.