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Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of unconverted material remaining. That is, if M grams is the amount of material converted after t minutes, then dM = k(S – M) where S grams is the initial amount of cane dT sugar and k is a constant. (i) Show that M = S + Ae¬kt satisfies the equation, where A is constant. (ii) If a certain amount of cane sugar is placed in water at time t = 0 and loges 40% of it has been converted after 10 minutes, show k =÷loge 10 3'

Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of unconverted material remaining. That is, if M grams is the amount of material converted after t minutes, then dM = k(S – M) where S grams is the initial amount of cane dT sugar and k is a constant. (i) Show that M = S + Ae¬kt satisfies the equation, where A is constant. (ii) If a certain amount of cane sugar is placed in water at time t = 0 and loges 40% of it has been converted after 10 minutes, show k =÷loge 10 3'

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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824/ Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of unconverted material remaining. That is, if M grams is the amount of material converted after t minutes, then dM = k(S – M) where S grams is the initial amount of cane dT sugar and k is a constant. (i) Show that M = S + Ae¬kt satisfies the equation, where A is constant. (ii) If a certain amount of cane sugar is placed in water at time t = 0 and 40% of it has been converted after 10 minutes, show k =- 5 loge 10 3
Transcribed Image Text:824/ Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of unconverted material remaining. That is, if M grams is the amount of material converted after t minutes, then dM = k(S – M) where S grams is the initial amount of cane dT sugar and k is a constant. (i) Show that M = S + Ae¬kt satisfies the equation, where A is constant. (ii) If a certain amount of cane sugar is placed in water at time t = 0 and 40% of it has been converted after 10 minutes, show k =- 5 loge 10 3
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