Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions
Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions
A metal ball is heated to a temperature of \(225{}^\circ \mathrm{C}\) before being dropped into a liquid. As the ball cools, its temperature, \(T{}^\circ \mathrm{C}\), \(t\) minutes after it enters the liquid is given by \(T=P+190{{\mathrm{e}}^{-kt}}\), where \(P\) and \(k\) are constants.
- Explain why \(P=35\).
When \(t=4\), the temperature of the ball reaches \(120{}^\circ \mathrm{C}\).
- Find the value of \(k\) correct to \(3\) significant figures.
- From the equation of T given above, explain why the temperature of the ball can never fall below \(35{}^\circ \mathrm{C}\).
Video Solution:
Video solution locked
A free account saves your progress; this video needs a course plan.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.
Create a free account to practise similar questions.
Answer:(a) \(P=35\). (b) \(k=0.201\) (3 s.f.). (c) \(T>35^\circ\mathrm C\) for finite \(t\), and \(T\to35^\circ\mathrm C\).
Need help? Join our A-Maths tuition classes.
Learn more