2. The population of a certain state is known to grow at a rate proportional to the number of people presently living in the state. If after 10 years the population has trebled and if after 20 years the population is 150,000, find the number of people initially living in the state.

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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Answer no. 2
Applications of Differential Equations of Order One
Solve the following:
1. In a certain culture of bacteria, the rate of increases is proportional to
the number present. (a) If it is found that the number doubles in 6
hours, how many may be expected at the end of 18 hours? (b) If
there are 10? at the end of 4 hours, and 8x10? at the end of 8 hours,
how many were there in the beginning?
2. The population of a certain state is known to grow at a rate
proportional to the number of people presently living in the state. If
after 10 years the population has trebled and if after 20 years the
population is 150,000, find the number of people initially living in the
state.
3. A cold beer initially at 35°F warms up to 40°F in 3 minutes while
sitting in a room of temperature 70°F. 'How warm will the beer be if
left out for 20 minutes?
Transcribed Image Text:Applications of Differential Equations of Order One Solve the following: 1. In a certain culture of bacteria, the rate of increases is proportional to the number present. (a) If it is found that the number doubles in 6 hours, how many may be expected at the end of 18 hours? (b) If there are 10? at the end of 4 hours, and 8x10? at the end of 8 hours, how many were there in the beginning? 2. The population of a certain state is known to grow at a rate proportional to the number of people presently living in the state. If after 10 years the population has trebled and if after 20 years the population is 150,000, find the number of people initially living in the state. 3. A cold beer initially at 35°F warms up to 40°F in 3 minutes while sitting in a room of temperature 70°F. 'How warm will the beer be if left out for 20 minutes?
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