Question

The population of bobcats in northern Arizona since 2008 can be modeled using the function b(t) = –0.32t2 + 2.7t + 253. What does t represent? What is the domain for this function? Which range values would not make sense for this function? Would the graph be continuous or discrete, and why?

Answer 1

Solution:  

In the given function b(t), the variable t represents the number of years after 2008. The   domain of this function is $[0,\infty )$. The range more than 258.7 would not make sense. The graph of the function is always continuous.

Explanation:

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 $[0,\infty )$.

The given function is a quadratic function and the coefficient of $t^2$ 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 $v(-\frac{b}{2a},f(-\frac{b}{2a}))$.

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.

Answer 2

1.the number of years since 2008 
2.t values greater than or equal to 0
3.negative values 
4.discrete,because number of bobcats cannot be broken to fractional parts