Biology Reference
In-Depth Information
the initial population size P
0
¼
5.3, the solution allows us to compute
directly the population P
n
for any value of n. For example, when n
¼
120,
we can use Eq. (1-8) to compute the model prediction for the U.S.
population in the year 3000:
120
10
16
P
120
¼ð
1
:
345
Þ
ð
5
:
3
Þ¼
1
:
48234
¼
14
:
8 quadrillion
:
How realistic do you think this prediction is? Why?
E
XERCISE
1-2
Use the continuous model from Eq. (1-7) to predict the U.S. population
in the year 3000. Is this prediction realistic? Why?
E
XERCISE
1-3
The data in Table 1-4 show the initial phase of yeast culture growth over
7 hours (Carlson [1913]; Pearl [1927]). The size of the yeast population is
measured in terms of biomass. Biomass is simply the weight of living
material. For yeast or bacteria, population growth may also be measured
by taking advantage of the fact that, as they grow, the medium in which
they are growing becomes increasingly turbid. A spectrophotometer is
used to determine the amount of light scattered by samples of the
culture.
(a) Use this data to determine the best values for k and r for the
discrete model (1-1) and the continuous model (1-2).
(b) Use the values determined in part (a) to create a table displaying
the actual and predicted values from the discrete and continuous
models.
(c) For the value of r determined in (a), plot the predictions of the
continuous model, and consider the graph. Based on the graph, do
you expect the continuous model to remain accurate in predicting
the long-term growth behavior of the culture?
Time
(hours)
0
1
2
3
4
5
6
7
Biomass
9.6
18.3
29.0
47.2
71.1
119.1
174.6
257.3
TABLE 1-4.
Growth of yeast population over 7 hours.
