Chapter 1, Problem 97P

The population of a culture of yeast cells is studied in the laboratory to see the effects of limited resources (food, space) on population growth, (a) Make a graph of the yeast population (measured as total mass of yeast cells) versus elapsed time. Draw a best-fit smooth curve, (b) After a long time, the population approaches a maximum known as the carrying capacity. Estimate the carrying capacity for this population, (c) When the population is much smaller than the carrying capacity, the growth is expected to be exponential: m(t) = m₀e^rt, where m is the population at any time t, m₀ is the initial population, r is the intrinsic growth rate (i.e., the growth rate in the absence of limits), and e is the base of natural logarithms (see Appendix A.3). To obtain a straight-line graph from this exponential relationship, we can plot the natural logarithm of m/m₀.

$In\frac{m}{m_0}=In{e}^{rt}=rt$

Make a graph of In (m/m₀) versus t from t = 0 to t = 6.0 h, and use it to estimate the intrinsic growth rate r for the yeast population.