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15 November, 18:30

12In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.

Find a quadratic model for the data in the table. Type your answer below. Show your work.

Time (hours)

0

1

2

3

4

5

6

Population (1000s)

5.1

3.03

1.72

1.17

1.38

2.35

4.08

+5
Answers (1)
  1. 15 November, 22:04
    0
    Let the equation be : at^2 + bt + c = P,

    where t = time (hrs),

    P = population (1000's).

    When t = 1, P = 3.03.

    When t = 2, P = 1.72.

    When t = 3, P = 1.17.

    Substitute these into the equation to obtain these 3 simultaneous equations : a + b + c = 3.03

    4a + 2b + c = 1.72

    9a + 3b = c = 1.17

    Solving gives:

    a = 0.38,

    b = - 2.45,

    c = 5.1.

    The equation is therefore,

    P = 0.38t^2 - 2.45t + 5.1

    Testing with t = 0 to 6 gives the population values as provided, so it seems to be a valid model.

    At t = 9 hrs,

    P = 0.38*9^2 - 2.45*9 + 5.1

    = 13.83.
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