A liquid is heated so that its temperature is x°C after 1 seconds. It is given thatthe rate of increase of x is proportional to (100-x). The initial temperature ofthe liquid is 25°C.a Form a differential equation relating x, 1 and a constant of proportionality,k, to model this information.bSolve 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 temperatureof the liquid after 195 seconds.d The model predicts that x cannot exceed a certain temperature. Write downthis maximum temperature.

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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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