2023 ACSBR AM S3 EOY Q1
2023 ACSBR AM S3 EOY Q1
Secondary 3
3 marks
An object is heated to a temperature of \(T{}^\circ\mathrm{C}\) before it is allowed to cool. The temperature of the object when it is cooling for \(t\) minutes can be modelled by \(T = 23 + 15e^{-\frac{3}{5}t}\).
- Find the value of \(t\) when \(T = 30\).[2]
- Explain why the temperature of the object will never go below \(23{}^\circ\mathrm{C}\).[1]
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Answer:(a) \(t=1.27\text{ min}\) (3 s.f.) (b) \(T>23{}^\circ\mathrm C\) for all \(t\)
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