Assignment 8: Log and Semi-log Review
1. A scientist recently discovered a new type of bacteria. Wishing to study the rate
at which the bacteria reproduced the scientist cultured a single bacterium and
counted the number of bacteria in the Petri dish every ten seconds. The following
table shows his results. Plot the number of bacteria vs. time on log-log paper.
Verify that the relationship is linear and find the slope and y-intercept.
Time
(seconds)
10
20
30
40
50
60
70
80
90
100
Number
Of
Bacteria
(N)
2
5
8
17
31
66
130
260
515
1030
1. Graph the data in the table below on semi-log y paper and complete the following:
a. Verify that the relationship ln(y) vs. x is linear.
b. Compute the slope and the y intercept.
c. Verify that the data can be represented by the exponential relationship
y  ab x where m  log b and log a  y 0 (where y 0 is the y-intercept).
d. Determine the actual exponential function.
x
y
2
4
6
8
10
40
284
1475
7655
68890