Colorado State University Population Growth Formulas Equations

For this discussion, you will be selecting one of the population growth formulas found in Chapter 6 of the course textbook.

TextBook:

https://openstax.org/books/college-algebra/pages/6…

Your task for this discussion is as follows:

Good evening,
For this week’s discussion, we were asked to analyze the population growth of any selected state. For my research and application, I decided on
the state of Delaware, which I am currently stationed in. After going through the U.S. Census Bureau, I discovered the population at the years
2010 and 2020. The population sizes were 897,934 and 989,948 respectively to the dates I previously mentioned. When solving for the rate of
growth constant I used, k = (In 989948)-(In 897934)
which gave me k = .00975558. Using 2010 as my initial population size, I can develop an
exponential function to represent the population growth with P (t) = 897934e(0.00975558)t which is graphed below.
10-0
2000000
1500000-
-1000000-
edit graph on
desmos
150
-50
50
100
Based off the function and graph, we get approximately a population size of 1,326,527 at the year 2050. Keep in mind that t = 40 was used
because the starting population was at the year 2010 and the time needed to reach 2050 was 40 years. Now the population will double at
approximately the year 2081 because it takes about 71 years of growth at the identified rate.
For other examples that use exponential or logarithmic functions, I would say the most common are monitoring compounding interest in
finances and the exponential decay for materials when in the field of chemistry. Again, I would say they are used more frequently and effectively
more than we realize it.Hello Everyone,
Texas populations’ growth rate has reportedly been consistent over the past few years, staying around a 1.1% increase, as seen from July 2020
to July 2021 (Hardison, 2021). To determine the expected population for Texas by the year 2050 I will use this growth rate (r), the current
population of Texas (estimated 29,500,000 million people), and the time difference between 2022 and 2050 (28 years) (t). I will calculate this
using the following equation:
P(T) = (Current Population) ert
= (29,500,000) 2.7180.011 (28)
= (29,500,000) 2.7180.308
= (29,500,000) 1.36
P(T) = 40,120,000
According to this calculation, the projected population for Texas in the year 2050 is expected to be 40,120,000 residents.
To determine when the population will double, I will use the doubling time equation. For the double time equation, I will take the natural
logarithm of 2, and divide this by the growth rate of 1.1% (k), and set that equal to the time (T) as seen below:
T = In 2
k
=
0.693
0.011
T = 63
According to this calculation, the population of Texas is expected to double in 63 years, or by the year 2085.
This is just one example of real-world context that can be modeled using exponential or logarithmic equations. However, you can also use the
doubling time equation to determine the growth rate of bacteria. While the exponential decay model can be used to determine radioactive
decay.
I hope you have a great week!