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7. Population of a Country The population of a country has a relative growth rate of 3% per year. The government is trying to reduce the growth rate to 2%. The population in 2011 was approximately 110 million. Find the projected population for the year 2036 for the following conditions. (a) The relative growth rate remains at 3% per year. (b) The relative growth rate is reduced to 2% per year.

7. Population of a Country The population of a country has a relative growth rate of 3% per year. The government is trying to reduce the growth rate to 2%. The population in 2011 was approximately 110 million. Find the projected population for the year 2036 for the following conditions. (a) The relative growth rate remains at 3% per year. (b) The relative growth rate is reduced to 2% per year.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 44EQ
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7. Population of a Country The population of a country has a relative growth rate of 3% per year. The government is trying to reduce the growth rate to 2%. The population in 2011 was approximately 110 million. Find the projected population for the year 2036 for the following conditions. (a) The relative growth rate remains at 3% per year. (b) The relative growth rate is reduced to 2% per year. 8. Bacteria Culture It is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 22. the projected population after 24 hours for the following ind conditions. (a) No antibiotic is present, so the relative growth rate is 12%. (b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%. 9. Population of a City The population of a certain city was 112,000 in 2014, and the observed doubling time for the pop- ulation is 18 years. (a) Find an exponential model n(t) = no2la for the popula- tion t years after 2014. (b) Find an exponential model n(t) = noe" for the popula- tion t years after 2014. (c) Sketch a graph of the population at time t. (d) Estimate how long it takes the population to reach 500,000.
Transcribed Image Text:7. Population of a Country The population of a country has a relative growth rate of 3% per year. The government is trying to reduce the growth rate to 2%. The population in 2011 was approximately 110 million. Find the projected population for the year 2036 for the following conditions. (a) The relative growth rate remains at 3% per year. (b) The relative growth rate is reduced to 2% per year. 8. Bacteria Culture It is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 22. the projected population after 24 hours for the following ind conditions. (a) No antibiotic is present, so the relative growth rate is 12%. (b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%. 9. Population of a City The population of a certain city was 112,000 in 2014, and the observed doubling time for the pop- ulation is 18 years. (a) Find an exponential model n(t) = no2la for the popula- tion t years after 2014. (b) Find an exponential model n(t) = noe" for the popula- tion t years after 2014. (c) Sketch a graph of the population at time t. (d) Estimate how long it takes the population to reach 500,000.
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