2
HW #23
6, 10, 11, 14, 15, 18, 19
4.6
GYPSY MOTHS
Biological populations can grow exponentially if not restrained by predators
or lack of food. The gypsy moth outbreaks that occasionally devastate the forests of the Northeast
illustrate approximate exponential growth. It is easier to count the number of acres defoliated by the
moths than to count the moths themselves.
Here are data on an outbreak in Massachusetts:
•
Let L1 = year,
L2 = acres
•
Look at scatterplot:
year vs acres,
scatterplot looks ___
exponential
__
•
Verify that
y
is being multiplied by about 4 each year by calculating the ratio of acres
defoliated each year to the previous year.
(start with 1979 to 1978, when the ratio is
226,260/63,042 = 3.59)
The ratios are 226,260/63,042 = 3.59, 907,075/226,260 = 4.01, and
2,826,095/907,075 =
3.12.
•
Let L3 = log (acres) = log (L2)
log
y
yields 4.7996, 5.3546, 5.9576, and 6.4512.
•
Look at scatterplot, year vs log (acres),
L1 vs L3
Year
Acres
1978
63,042
1979
226,260
1980
907,075
1981
2,826,095