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?
Would the graph be continuous or discrete, and why?

Answer 1

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

Answer 2

A) t represents time ( in years ) since 2008( 2008 is zero-year)
B) Domain for the square function is x∈R, but for this kind of function there are only positive values. Firs we will find interceptions with x-axis :

`t_(12) = \frac{-b\pm \sqrt{ b^(2)-4ac } }{2a}`

`t_(12) = \frac{-2.7\pm \sqrt{ 2.7^(2)-4*(-0.32)*253 } }{-0.64}`
(calculate), t1=-24.22, t2=32.65
Domain for this function is: 0 ≤ t ≤32.65
C) The graph is discrete, because it is only in the first quadrant ( doesn`t have negative values ( i.e. you can`t have -10 bobcats in northern Arizona.