Rabbit Population Dynamics and Functions

The video tutorial explains how to model a rabbit population that oscillates above and below an average value throughout the year. The population starts at 750 rabbits and increases by 100 each year. The tutorial derives an equation for the population in terms of months since January, combining a trigonometric function for oscillation and a linear function for growth. The trigonometric part uses a cosine function with a period of 12 months and an amplitude of 60, while the linear part accounts for the annual increase in population. The final equation is presented, and its graph is discussed.

What is the average starting population of rabbits?

• 750

• 700

• 600

• 800

How much does the average rabbit population increase each year?

• 125

• 100

• 75

• 50

What trigonometric function is used to model the oscillation of the rabbit population?

• Sine

• Tangent

• Secant

• Cosine

What is the period of the trigonometric function used in the rabbit population model?

• 18 months

• 24 months

• 12 months

• 6 months

What is the amplitude of the oscillation in the rabbit population model?

• 45

• 75

• 30

• 60

What is the value of 'A' in the trigonometric equation for the rabbit population?

• -60

• 60

• -30

• 30

What is the slope of the linear part of the rabbit population equation per month?

• 100/3

• 50/3

• 25/3

• 75/3

What is the y-intercept of the linear part of the rabbit population equation?

• 750

• 800

• 700

• 600

What does the complete population equation account for?

• Only oscillation

• Only linear growth

• Both oscillation and linear growth

• Neither

How does the graph of the complete population equation appear?

• Constant

• Purely oscillatory

• Linear with oscillation

• Purely linear