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3 May, 12:10

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?

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  1. 3 May, 14:57
    0
    Step-by-step 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.
  2. 3 May, 16:04
    0
    "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.
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