Chapter 3.4, Problem 47P

(a)

To determine

To calculate:

The growth rate of the bacteria in a $2\cdot {10}^{-4}$ molar glucose solution if the growth rate of the E coli bacteria in a solution is given by $R=\frac{1.35C}{0.22+C}$ cell division per hour. Cis the concentration of glucose in the solution.

(b)

To determine

To calculate:

The value of $\frac{dR}{dC}$ if the growth rate of the E coli bacteria in a solution is given by $R=\frac{1.35C}{0.22+C}$ cell division per hour. Cis the concentration of glucose in the solution.

(c)

To determine

To calculate:

The value of ${\frac{dR}{dC}|}_{C=2}$ if the growth rate of the E coli bacteria in a solution is given by $R=\frac{1.35C}{0.22+C}$ cell division per hour. Cis the concentration of glucose in the solution.

(d)

To determine

To calculate:

The linear approximation of the growth rate for bacteria growing in glucose concentrations near $C=2$ if the growth rate of the E coli bacteria in a solution is given by

$R=\frac{1.35C}{0.22+C}$ cell division per hour. Cis the concentration of glucose in the solution.

(e)

To determine

To calculate:

The linear approximation of the growth rate for bacteria growing in glucose concentrations near $C=2.2$ and compare with the original results if the growth rate of the E coli bacteria in a solution is given by $R=\frac{1.35C}{0.22+C}$ cell division per hour. Cis the concentration of glucose in the solution.