Q3(a)A polluted pool has an initial concentration of bacteria of 10* part/m³, while theacceptable level is only 5 x 103 part/m³. The concentration of the bacteria willreduce as fresh water enter the pool. The differential equation that governs theconcentration C of the pollutant as a function of time (in weeks) is given by:dC+ 0.05C = 0,dtC(0) = 10*(i)Estimate the concentration of the pollutant after 15 weeks by taking a stepsize of 1 week.(ii)Find the absolute error if the exact solution of Q3(a)(i) isC(t) = 10*e-0.05£

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Answered: Q3 (a) A polluted pool has an initial…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 13EQ

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yn-y'=lotcOS(2€)
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When a transistor radio is switched off the current I (in milliseconds) falls away according to the differential equation dI/dt=-0.4I where t is the time in milliseconds. At the instant the radio is switched off the current is 350milliseconds. Write an equation for I in terms of the. Find the current after 5 milliseconds How long will it take for the current to fall to 20milliamps
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A water balloon of mass 890 grams is rolled on level ground with an initial velocity of 38 meters per second. As it travels, water leaks from the balloon at a rate of 255 grams per second. Assume air resistance is proportional to velocity with coefficient 6 grams per second. (a) Find the velocity of the balloon as a function of time. v(t) = (b) What is the furthest distance the balloon could travel? Total distance = meters.

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