(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°.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...

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Question

Please do A and B

(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 108 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°.

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