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The temperature, \(T\), of a cup of coffee is recorded at various times, \(t\), after it is poured. The data is shown in the table below.
\(t\) (minutes) 0 2 5 9
\(T\) (°C) 90 75 60 50
  1. Find the average rate of change of the temperature:
    1. between \(t=0\) and \(t=2\) minutes.
    2. between \(t=2\) and \(t=5\) minutes.
    3. between \(t=5\) and \(t=9\) minutes.
  2. What do these rates of change suggest about how the coffee is cooling?

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