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The temperature T(t)°C of an object at time t seconds is modelled using Newton’s Law of Cooling - HSC - SSCE Mathematics Extension 1 - Question 1 - 2023 - Paper 1

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The temperature T(t)°C of an object at time t seconds is modelled using Newton’s Law of Cooling. T(t) = 15 + 4e^{-3t}; What is the initial temperature of the objec... show full transcript

Worked Solution & Example Answer:The temperature T(t)°C of an object at time t seconds is modelled using Newton’s Law of Cooling - HSC - SSCE Mathematics Extension 1 - Question 1 - 2023 - Paper 1

Step 1

What is the initial temperature of the object?

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Answer

To find the initial temperature of the object, we set time t to 0:

T(0)=15+4e−3(0)T(0) = 15 + 4e^{-3(0)}

This simplifies to:

T(0)=15+4e0T(0) = 15 + 4e^{0}

Since e0=1e^{0} = 1, we have:

T(0)=15+4(1)=15+4=19T(0) = 15 + 4(1) = 15 + 4 = 19

Thus, the initial temperature of the object is 19°C.

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