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mixer [17]
3 years ago
7

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)=7

5+.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))=
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
5 0

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}.

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