Chapter 9.4, Problem 21E

Dialysis A model that estimates the concentration of urea in the body for a particular dialysis patient, following a dialysis session is given by

$C\left(t,g\right)=0.6{\left(0.96\right)}^{\left(210t/1500\right)-1}+\frac{gt}{126t-900}\left[1-{\left(0.96\right)}^{\left(210t/1500\right)-1}\right].$

Where $t$ represents the number of minutes of the dialysis session and $g$ represents the rate at which the body generates urea in mg per minute. Source: Clinical Dialysis.

a. Find $C\left(180,8\right).$

b. Using the total differential, estimate the urea concentration if the dialysis session of part was cut short by $10$ minutes and the urea generation rate was $9$ mg per minute. Compare this with the actual concentration. (Hint: First, replace the variable $g$ with the number $8$, this reducing the function to one variable. Then use your graphing calculator to calculate the partial derivatives $C_t\left(180,8\right)$. A similar procedure can be done for $C_g\left(180,8\right).)$

c.

d.