Math Project #2 0416
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Feb 20, 2024
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Math Project #2 : Modeling W/ Functions
Cassi Owner
1.
Create three different graphs for each set of data. (nine graphs total). For example, you may use a bar graph, a scatterplot, a line graph, or a circle graph. What do you notice about the data? Compare and contrast the sets of data.
FLORIDA
PENNSYLVANIA
WEST VIRGINIA
2.
Which model would best represent each set of data: linear, quadratic, or exponential? Explain your reasoning based on your graphs.
Florida- The model that best represents Florida’s data set is an exponential model. I say this because the amount of people living in florida grew quickly and it continued to over the years. In all three of the graphs you can see how quickly the numbers went up. Pennsylvania-
The model that best represents Pennsylvania’s data set is a linear model. I say this because the number of residents in PA
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was relitively the same over the years with small increases in the recent years. West Virgina-
The model that best represents West Virginia’s data set is a linear model. The reason I say this is because similar to PA the numbers have been constant over the years except with WV numbers went down slightly in recent years. 3.
Determine the average rate of change for each set of data from 1910 to 2020. What do you notice? Compare and contrast the growth rates for the states. How do you think these growth rates will impact government allocations for each state?
This can be found by subtracting the first and last amount of population and dividing that by the first and last year. Florida
- The average rate of change for Florida is 0.189 or 18.9%
(
21.54-0.75)/(2020-1910)=0.189
Pennsyvania- The average rate of change for Pennsyvania is 0.0484 or 4.84%
(13-7.67)/(2020-1910)=0.0484 West Virginia
- The average rate of change for West Virginia is 0.005 or 5%
(1.79-1.22)/(2020-1910)= 0.005
The growth rates reflect the same oberservations as the graphs. Florida has the biggest growth rate as we know it had the largest rate of change. Pennsyvania and West Virginia both stayed constant for the most part. These
growth rates, especially Florida, will impact the government allocations because more recources will be needed as the population goes up, along with government funding.
4.
Determine an exponential model for the states with the two fastest growth rates. Explain your work. Note: The y-intercept equals the value
provided for 1910. Thus, for the year 1910, x = 0.
Y=abx--- The two fastest rates of change is Florida and West Virgina
Florida- (21.54)
y=0.75*0.189^{110}
Using the model above I plugged in the number. The current population for y (21.54) a is the initial population (0.75) b is the rate of change (0.189) and the number of years for 110
West Virgina- (1.79) y=1.22 *0.005^{110}
Using the model above I plugged in the numbers. The current population for y (1.79) a is the initial population (1.22) b is the rate of change (0.005) and the number of years is 110
5.
Use your exponential models to predict the populations for these two states for the year 2030 (x = 120, the number of years since 1910). Explain your work. Do your predictions seem reasonable? Explain your reasoning.
To find the populations for both states in year 2030 I will just plug in 120 into
the equation instead of 110. Florida-
(21.54)
y=
0.75*0.189^{120}= 1.52 m
West Virginia -
(1.79) y=1.22 *0.005^{120}=9.17 m
I do not think my predictions are reasonable. For one Florida’s 2030 population should be signicicantly higher then WV based on the trends. Also Florida’s population in 2030 seems low all together.