Question

Analyzing a Function 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

Explanation:

a). t represents the number of years after year 2008.

b). The given function is b(t) = -0.32t²+ 2.7t + 253

Domain of this function all real numbers greater than zero

t ≥ 0

c). Fof t = 0

b(0) = -3.2(0) + 2.7(0) + 253

= 253

Therefore, range of the given function is all real numbers greater than 253.

b ≥ 253

d). Graph of the given function represents population.

Value of b should be in whole numbers. But when we solve the equation for different values of t, we get the value of b in fraction.

Therefore, graph will be a discrete graph.

Answer 2

"b" represents the population of bobcats.

1) "t" represents the number of years after 2008.

2) The domain (t) starts at 0 (which is the year 2008) ⇒ t ≥ 0

3) The range (b) starts when t = 0. b =-0.32(0)² + 2.7(0) + 253 ⇒ b ≥ 253

4) The graph is discrete because the population must be in whole numbers.