Coffee Cooling Model – ++ Prep

Coffee Cooling Model

00:00 6 marks

The temperature, \(T\) °C, of a cup of coffee \(t\) minutes after it is poured is given by the function

\[T(t) = 20 + 65e^{-0.04t}.
\]

(a) Write down the initial temperature of the coffee when it is poured (\(t = 0\)). [1]

(b) Find the temperature of the coffee after 10 minutes. [2]

(c) Find the time it takes for the temperature to reach 50 °C. [3]

Part a

1 minutes 1 marks

Question

Write down the initial temperature of the coffee when it is poured (t = 0). [1]

Hint Hint

Hint

Substitute \(t = 0\) into the given formula

Answer Answer
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Complete Answer

85 °C

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Part b

2 minutes 2 marks

Question

Find the temperature of the coffee after 10 minutes. [2]

Hint Hint

Hint

Substitute \(t = 10\) and evaluate the exponential

Answer Answer
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Complete Answer

63.6 °C

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Part c

4 minutes 3 marks

Question

Find the time it takes for the temperature to reach 50 °C. [3]

Hint Hint

Hint

Set \(T(t)=50\) and use \(\ln\) to solve for \(t\)

Answer Answer
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Answer Answer

Complete Answer

19.3 minutes

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