The population of bobcats in northern Arizona since 2008 can be modeled using the function b(t) = –0.32t2 + 2.7t + 253.

In the given function b(t), the variable t represents the number of years after 2008. The   domain of this function is . The range more than 258.7 would not make sense. The graph of the function is always continuous

The given function b(t) shows the population of bobcats in northern Arizona since 2008. Therefore the variable t represents the number of years after 2008.

Since t represents the number of years after 2008, which is either positive or zero, therefore the domain of this function is .

The given function is a quadratic function and the coefficient of  is negative, so it is a downward parabola. The range above the y-coordinate of the vertex doesn't make any sense.

The vertex of parabola is defined by .

Vertex of the given function is (4.2,258.7).

Thus, the range more than 258.7 would not make sense for this function.

Since the given function is a polynomial function and polynomial functions are always continuous, therefore the graph of the function is always continuous

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d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day