Mathematics: 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))=

3,4,2,5,1Step-by-step explanation:...

The effect of caffeine, c, in milligrams, on a

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10.03.2022

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

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