1) The population of a certain country is known to increase at a rate proportional to the number of people presently living in the country. If after two years the population has doubled, and after three years the population is 20,000, estimate the number of people initially living in the country. Ans: 7,062 (Bronson & Costa, 2006)

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Chapter1: Functions And Models
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Establish the governing first-order differential equation based on physical principles
underlying the problem and find the solution as required. Show all the pertinent
solutions.
1) The population of a certain country is known to increase at a rate proportional
to the number of people presently living in the country. If after two years the
population has doubled, and after three years the population is 20,000, estimate
the number of people initially living in the country. Ans: 7,062 (Bronson &
Costa, 2006)
2) A bacteria culture is known to grow at a rate proportional to the amount present.
After one hour, 1000 strands of the bacteria are observed in the culture: and
after four hours, 3000 strands. Find (a) an expression for the number of strands
of the bacteria present in the culture at any timet and (b) the number of strands
of the bacteria originally in the culture. Ans: (a) N = cekt; (b) 694 (Fogiel, 1994)
%3D
3) A certain radioactive material loses mass at a rate proportional to the mass
present. If the material has a half-life of 30 minutes, what percent of the original
mass is expected to remain after 0.9 hour? Ans: 29% of the original (Fogiel,
1994)
Transcribed Image Text:Establish the governing first-order differential equation based on physical principles underlying the problem and find the solution as required. Show all the pertinent solutions. 1) The population of a certain country is known to increase at a rate proportional to the number of people presently living in the country. If after two years the population has doubled, and after three years the population is 20,000, estimate the number of people initially living in the country. Ans: 7,062 (Bronson & Costa, 2006) 2) A bacteria culture is known to grow at a rate proportional to the amount present. After one hour, 1000 strands of the bacteria are observed in the culture: and after four hours, 3000 strands. Find (a) an expression for the number of strands of the bacteria present in the culture at any timet and (b) the number of strands of the bacteria originally in the culture. Ans: (a) N = cekt; (b) 694 (Fogiel, 1994) %3D 3) A certain radioactive material loses mass at a rate proportional to the mass present. If the material has a half-life of 30 minutes, what percent of the original mass is expected to remain after 0.9 hour? Ans: 29% of the original (Fogiel, 1994)
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