(a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i) If it is found that the number doubles in 8 hours, how many may be expected at the end of 24 hours? (ii) If there are 10® at the end of 7 hours and 4 × 10° at the end of 9 hours, how many were there in the beginning? (b) According to Newton's law of cooling, the rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of the air. If the temperature of the air is 32° and the substance cools from 100° to 70° in 15 minutes, find when the temperature will be 42°.
(a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i) If it is found that the number doubles in 8 hours, how many may be expected at the end of 24 hours? (ii) If there are 10® at the end of 7 hours and 4 × 10° at the end of 9 hours, how many were there in the beginning? (b) According to Newton's law of cooling, the rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of the air. If the temperature of the air is 32° and the substance cools from 100° to 70° in 15 minutes, find when the temperature will be 42°.
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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