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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?

Verified Answer :

HomertheGenius
At 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 ( doesnt have negative values ( i.e. you cant have -10 bobcats in northern Arizona.
cheyennebaesa41

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


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