Question

The population size, P,
of owls (predators) in a certain region can
be modelled by the function
P(t) = 1000 + 100 sin (3.14t/12), where t represents
the time in months. The population size, p,
of mice (prey) in the same region is given by
p(t) = 20 000 + 4000 cos (3.14t/12). State the period, amplitude and vertical displacement for each curve. Graph both functions.

Answer 1

I will do the first, you do the second

P(t) = 1000 + 100 sin(πt/12)
period = 2π/(π/12) = 24 months
amplitude = 100
vertical displacement = 1000

Answer 2

period = 2ð/(ð/12) = 24 months
amplitude = 4000
vertical displacement = 20 000

Answer 3

correct