Cerebrospinal fluid is continually produced and reabsorbed by the body at a rate

Question

Cerebrospinal fluid is continually produced and reabsorbed by the body at a rate that depends on its current volume. A medical researcher finds that absorption occurs at a rate of 0.36 mL/min when the volume of fluid is 146 mL and at a rate of 0.13 mL/min when the volume is 46 mL. (a) Suppose the absorption rate A is a linear function of the volume V. Sketch a graph of A(V) 0.5 Abs. Rate (mL./min) Abs. Rate (mL/min) 150 0.4 100 0.3 0.2 50 0.1 Volume (mL) 0 0.0 Volume (mL) 150 0.1 0.2 0.3 0.4 0.5 0.0 50 100

Explanation / Answer

we have two points ( 146 , .36 ) and ( 46, .13)

slope = .13- .36 / 46 - 146

=.0023

hence, the equation is

y = .0023 x + .0242

3rd graph is correct

b) slope = 0.0023 min ^-1

in this case A increases by .0023 mL / min

c) A intercept of the graph is 0.0242 mL/ min

the A intercept is the initial rate of absorption corresponding to cerebrospinal fluid volume of 0 mL

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