Answer:
The composite function is [tex]r(c(t))=75+17.25e^{-0.1215t}[/tex].
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
[tex]r(c)=75+0.05c[/tex] .... (1)
The dissipation of caffeine from the bloodstream over time since ingestion, t, in hours can be modeled by the function
[tex]c(t)=345e^{-0.1215t}[/tex] .... (2)
We have to find the composite function r(c(t)).
Using equation (1), we get
[tex]r(c(t))=r(345e^{-0.1215t})[/tex]
Using equation (2), we get
[tex]r(c(t))=75+0.05(345e^{-0.1215t})[/tex]
[tex]r(c(t))=75+17.25e^{-0.1215t}[/tex]
Therefore the composite function is [tex]r(c(t))=75+17.25e^{-0.1215t}[/tex].
