Question

Most breeding birds in the northeast US migrate elsewhere during the winter. The number of bird species on an Ohio preserve oscillates between a high of 30 in June, and a low of 10 in December. Find a formula for the number of bird species B as a function of t months since January.

i) amplitude

ii) period

iii) Average value

iv) Horizontal shift

Answer 1

The answer is below

Explanation:

The function B can be represented by the function:

B = C + Acos(Pt)

a) From the graph of the function, it starts from 30, hence it is a cosine function.

The amplitude (A) = (highest value - lowest value) / 2 = (30 - 10) / 2 = 10

A = 10

b) The function completes an oscillation every 12 months, hence its period (P) = 12

c) The average value = 10/√2

d) The vertical shift (C) is the difference between the highest and lowest value.

Therefore, C = 30 - 10

C = 20