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 6 hours, how many may be expected at the end of 18 hours? (ii) If there are 106 at the end of 4 hours and 8 × 106 at the end of 7 hours, how many were there in the beginning?

Principles Of Radiographic Imaging: An Art And A Science
6th Edition
ISBN:9781337711067
Author:Richard R. Carlton, Arlene M. Adler, Vesna Balac
Publisher:Richard R. Carlton, Arlene M. Adler, Vesna Balac
Chapter8: X-ray Production
Section: Chapter Questions
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(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 6 hours, how many may be expected
at the end of 18 hours?
(ii) If there are 106 at the end of 4 hours and 8 × 106 at the end of 7 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°.

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