Question

Hello, everyone. I'm not very sure about this question, so can you please give me a hint for this question? Thanks!

Glucose is fed intravenous injection at a constant rate, k, into a patient's bloodstream. Once there, the glucose is removed at at rate proportional to the amount of glucose present. If R is the net rate at which the quantity, G, of glucose in the blood is increasing:
a) Write a formula giving R as a function of G
b) Sketch a graph of R against G.

P.S. I cannot understand what R is.

Answer 1

The amount of glucose=x\[\frac{dx}{dt}=k-cx\]

Answer 2

Do you know anything about differential equations?

Answer 3

Hello. Well, I do know about them, but this was supposed to be PreCalculus stuff.

Answer 4

I think this requires at least knowledge of exponential growth (thus differentiation).

Answer 5

Rate in = k. Rate out = mG (where m is the constant of proportionality; standard convention is to use k for that constant but we've already used that letter). Hence, R = k - mG.

Answer 6

The only way to do it without calculus (*I think*) is to assume that\[x=Ae^{qt}\]

Answer 7

a

Answer 8

Oh no, re-read the question, I'm overcomplicating most probably.

Answer 9

b

Answer 10

Wait, I don't have to use anything like exponential growth?

Answer 11

I was overcomplicating, it's only implicit in your question. It makes it much easier to solve, though.

Answer 12

And it's not quite normal exponential growth: I guess the constant q is imaginary, so by Euler's formula is a trig function.