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) = n,2la for the popula- tion t years after 2014. (b) Find an exponential model n(t) tion t years after 2014. (c) Sketch a graph of the population at time t. = noe" for the popula- (d) Estimate how long it takes the population to reach 500,000.
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) = n,2la for the popula- tion t years after 2014. (b) Find an exponential model n(t) tion t years after 2014. (c) Sketch a graph of the population at time t. = noe" for the popula- (d) Estimate how long it takes the population to reach 500,000.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Sec4.6:#9
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c34de7e-5935-4303-bb64-ce025f7422a2%2Fe57adab6-f986-4765-863c-d6dc64327608%2Fgahiuyp_processed.jpeg&w=3840&q=75)
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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