Chapter 2, Problem 2.33P

Interpretation Introduction

(a)

Interpretation:

The units of the specific growth rate should be determined.

Concept introduction:

The growth of cells in a bioreactor is defined as the function,

$X=X_0\exp \left(\mu t\right)$

Where X is the concentration of cells at any time t, X₀ is the starting concentration of cells and µ is the specific growth rate.

It is assumed that the given equation is valid and therefore dimensionally homogeneous. So, the dimension of the left hand side and right hand side of the equation is equal. In addition, the exp () component is dimensionless.

Interpretation Introduction

(b)

Interpretation:

Give two ways to plot the data so as to obtain a straight line.

Concept introduction:

The growth of cells in a bioreactor is defined as the function,

$X=X_0\exp \left(\mu t\right)$

Where X is the concentration of cells at any time t, X₀ is the starting concentration of cells and µ is the specific growth rate.

Interpretation Introduction

(c)

Interpretation:

The data should be plotted, and specific growth rate should be determined.

Concept introduction:

The growth of cells in a bioreactor is defined as,

$X=X_0\exp \left(\mu t\right)$

$\frac{X}{X_0}=\exp \left(\mu t\right)$

The data is given as,

Time, t(h)	Yeast Concentration, X (g/L)
0	0.01
4	0.048
8	0.152
12	0.733
16	2.457

Interpretation Introduction

(d)

Interpretation:

The time required for the yeast population to double should be determined.

Concept introduction:

The growth of cells in a bioreactor is defined as,

$X=X_0\exp \left(\mu t\right)$

$\frac{X}{X_0}=\exp \left(\mu t\right)$