MTH122 Peer discussion responses 200 words each

Need help with my Algebra question – I’m studying for my class.

Please reply to both POST1 and POST2 in at least 200 words each

POST1:

Good morning,

The state I have chosen to write about is my home state of Louisiana, one of the most unique states in the union, and the best when it comes to parties and food in my humble opinion. The population during the 2010 census was 4,533,372, and another current estimate I found for 2019 was 4,652,581 (Louisiana Population 2020, 2019). We currently have the 27th growth rate in the country currently, at a whopping 0.75%.

To find the population estimate for the year 2050, I used the formula from the lecture with the 2019 estimate I had found:

P(t) = P0ert = 4,652,581 e (0.0075)(31) = 5,870,396.153

Seeing as people are whole, I’ll round down to 5,870,396 people in the great state of Louisiana in 2050.

To find out when the population will double, I again used the 2019 estimate and put in the following equation:

P(t) = P0ert, 9,305,162 = 4,652,581 e (0.0075)t = 92.4 years

In all probability, I will not be around in 92 years to see that population, I just hope that the crawfish population will be able to keep up with that demand.

I can see that there are plenty of uses for exponential growth and logarithmic functions. The bank uses exponential relationships to figure out how much a loan repayment is. Growing up with photography, I never realized that the formulas used to measure an exposure were logarithmic.

Craig

References

Louisiana Population 2020 (2019, June 19). Retrieved from http://worldpopulationreview.com/states/louisiana-population/

POST2:

Hello Class,

I will be calculating the population growth of the state of Georgia because this is my home state. Some interesting information that I have learned is that Georgia is the 24th largest US state, the 12th fastest growing state with the 10th fastest population growth rate at 1.19%. I gathered more recent and accurate population data from the US Census Bureau, as reported by the American Community Survey, the estimated population as of the year 2019 was 10,617,432.

The Population Growth function is LaTeX: Pleft(tright)=P_0e^{kt}

P

(

t

)

=

P

0

e

k

t

and the equation is as follows:LaTeX: Pleft(tright)=10.6e^{0.0119t}

P

(

t

)

=

10.6

e

0.0119

t

To find the population for 2050, I determined the years after the recorded year of 2019 is 51 years, so t=51 for LaTeX: Pleft(51right)=10.6e^{0.0119left(51right)}=10.6e^{0.6069}approx19.4

P

(

51

)

=

10.6

e

0.0119

(

51

)

=

10.6

e

0.6069

19.4

In the year 2050, the population of Georgia will be approximately 19,400,000.

To determine the double-time or the year when the population will be 21,200,00 the equation is as follows: LaTeX: 21.2=10.6e^{0.0119t}

21.2

=

10.6

e

0.0119

t

LaTeX: frac{21.2}{10.6}=e^{0.0119t}

21.2

10.6

=

e

0.0119

t

LaTeX: lnfrac{21.2}{10.6}=ln e^{0.0119t}

ln

21.2

10.6

=

ln

e

0.0119

t

LaTeX: ln2=0.0119t

ln

2

=

0.0119

t

LaTeX: frac{ln2}{0.0119}=t

ln

2

0.0119

=

t

LaTeX: tapprox58.2

t

58.2

The population will double to 21.2 million in approximately 58 years from 2019, so this will be the year 2057.

I have learned many different real-world situations that call for the use of exponential and logarithmic functions. I can imagine that since we can determine the state population growth using exponential functions we can also determine that of animals or such as in Florida the over-populating iguana epidemic considered an invasive species.

I never thought I would ever understand how to use the exponential or logarithmic functions, but I have found it to be fairly since I have gotten the hang of it.

References

U.S. Census Bureau (2019). Georgia population estimates. QuickFacts. Retrieved from https://www.census.gov/quickfacts/fact/table/GA/PS…

World Population Review. (2019). Georgia population. Retrieved from http://worldpopulationreview.com/states/georgia-po…

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