A liquid is heated so that its temperature is xC after t seconds. It is given that
Question:
A liquid is heated so that its temperature is x°C after t seconds. It is given that the rate of increase of x is proportional to (100 − x).
The initial temperature of the liquid is 25°C.
a. Form a differential equation relating x, t and a constant of proportionality, k, to model this information.
b. Solve the differential equation and obtain an expression for x in terms of t and k.
c. After 180 seconds the temperature of the liquid is 85°C. Find the temperature of the liquid after 195 seconds.
d. The model predicts that x cannot exceed a certain temperature. Write down this maximum temperature.
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a Let the temperature of the liquid be x at time t and let k be the constant ...View the full answer
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Related Book For 
Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook
ISBN: 9781108407199
1st Edition
Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey
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