Analysis of Maryland Population Growth - Essay Example

The population of Maryland 10 years from now (in the year 2022):
For year 2022, n = 2022 – 2010 = 12. Therefore,
P2022 = P(1 + r)n
= 5,773,552(1 + 0.009)12
= 5,773,552(1.009)12
= 5,773,552(1.1135)
= 6,428,906

The population of Maryland 10 years from now (in the year 2022) will be around 6,428,906.
The time (in years) and year, the population in Maryland may double:
2P = P(1 + r)n
2(5,773,552) = 5,773,552(1 + 0.009)t
Dividing both sides by 5,773,552
2 = (1.009)n
Taking a log of both sides of the equation
log 2 = log (1.009)n
log 2 = n log (1.009)
Dividing both sides of the equation by log (1.009)
n = (log 2)/(log 1.009)
Using the logarithm function of a calculator,
n = (0.3010)/(0.0039) = 77.4
Therefore, it will take around 76 years (77.4 – 2 = 75.4) and in the year 2088 (= 2012 + 76), the population in Maryland may double assuming a steady annual growth rate of 0.9%.
The estimated population of Garrett County in which I live in the year 2011 was 30,051. The annual growth rate for my home county is -0.2%. Thus, the population in Garrett County is declining. Since the annual growth rate for my home county is negative; therefore, using this value, the population of my home county will never double. Therefore, the annual growth rate for Garrett County same as the Maryland state which is 0.9%.

The population of Garrett County in 10 years:
For year 2022, n = 2022 – 2011 = 11. Therefore,
P2022 = P(1 + r)n
= 30,051(1 + 0.009)11
= 30,051(1.009)11
= 30,051(1.1036)
= 33,164
The population of Garrett County in 10 years (in Year 2022) will be around 33,164 assuming a steady growth rate of 0.9%.
The time (in years) and year, the population in Garrett County may double:

2P = P(1 + r)n
2(30,051) = 30,051(1 + 0.009)t
Dividing both sides by 30,051
2 = (1.009)n
Taking a log of both sides of the equation
log 2 = log (1.009)n
log 2 = n log (1.009)
Dividing both sides of the equation by log (1.009)
n = (log 2)/(log 1.009)
Using the logarithm function of a calculator,
n = (0.3010)/(0.0039) = 77.4
Therefore, it will take around 77 years (77.4 – 1 = 76.4) and in the year 2089 (= 2012 + 77), the population in Garrett County may double assuming a steady annual growth rate of 0.9%.

The factor that could influence the growth rate of my city is the migration of people into or outside the county and state. I live in a county that is experiencing an annual decline of 0.2%, however, my state Maryland is experiencing an annual growth of 0.9%.
I may live in a city or state where the population is on the decline or has not changed. This is true for my county, which is experiencing a decline in the population.
Suppose there is a steady decline in the population of Garrett County, then the population of Garrett County in 10 years:

P2022 = P(1 + r)n
= 30,051(1 - 0.009)11
= 30,051(0.991)11
= 30,051(0.9053)
= 27,206
The population of Garrett County in 10 years (in Year 2022) will be around 27,206 assuming a steady decline rate of 0.9%.
The real-world applications where exponential equations can be utilized are radioactive decay and carbon dating for determining the age of bone and fossils. Read More