Summary:
Suppose inulin is infused into an individual until a steady-state concentration of 0.1g/(100 mL blood) is obtained. After steady-state is achieved, the inulin infusion is halted. With a catheter and sampling devices, you are able to take the instantaneous inulin concentration in the urine as well as the mixing cup average of the inulin in the urine (a mixing cup average is the average concentration of all the samples collected up to a specified time) Over a 2 hour period 180 mL of urine is collected with an average inulin concentration of .08g/mL.

Given:
- m, urine, inulin = 14.4 g
- C, urine, inulin = 0.08 g inulin / mL urine
- V, urine = 180 mL urine
- V, blood in = 14,400 mL
- GFR = 120 mL / min

Questions:
a) Determine the length of time until the instantaneous concentration of inulin in the blood drops to 1/10 th if its original concentration.
b) Use an integral mass balance to show that the total mass of inulin excreted in the urine is equivalent to the mass of inulin initially in the blood.
c) Derive an equation describing the mixing cup inulin concentration as a function of time, blood volume, GFR (volume of blood filtered per unit time)or(Glomerular Filtration Rate), collected urine volume, and other variables that you find necessary.
d) At what time does the mixing cup inulin concentration equal the instantaneous inulin concentration
e) At what time does the mixing cup inulin concentration equal two times the instantaneous inulin concentration?