(b) Find a sine curve that models the data (as in Example 1).

Question

When two species interact in a predator/prey relationship, the populations of both species tend to vary in a sinusoidal fashion. (See Discovery Project: Predator/Prey Models referenced on page 427). In a certain midwestern county, the main food source for barn owls consists of field mice and other small mammals. The table gives the population of barn owls in this county every July 1 over a 12-year period.

Year
0	50
1	62
2	73
3	80
4	71
5	60
6	51
7	43
8	29
9	20
10	28
11	41
12	49

Answer 1

The axis is 50 with a high of 80 and a low 20 so the amplitude is 30.

The periodi is 12 years so B = 2pi/12 = pi/6

y = 30 Sin (pi/6)x + 50

Note: y is the population of barn owls and x is the years.