This portfolio is an investigation into how the median Body Mass Index of a girl will change as she ages. Body Mass Index (BMI) is a comparison between a person's height (in meters) and weight (in kilograms) in order to determine whether one is overweight or underweight based on their height. The goal of this portfolio is to prove of disprove how BMI as a function of Age (years) for girls living in the USA in 2000 can be modeled using one or more mathematical equations. This data can be used for parents wanting to predict the change in BMI for their daughters or to compare their daughter's BMI with the median BMI in the USA.
The equation used to measure BMI is:
The chart below shows the median BMI for girls of different ages in the
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That can be fixed by adjusting the horizontal phase shift value of _c_ to 12.4 to compensate.
There is also a noticeable discrepancy between the function graph and the scatter plot in the domain {} and {}. A slight stretch about the y axis would fit the curve closer to the data points in those areas, therefore the _b_ value should be changed from π/15 to π/14. The number π/14 was chosen because reducing the denominator's value by 1 will increase the b value by a slight amount, and an increased b value will shorten period and compress the graph about the y axis, resulting in the values within domain to be closer to that of the data points.
Making these changes, the revised formula for the sinusoidal function is as follows:
Using TI InterActive!™ to graph that function, overlaid with the original data, and restricting the graph of the function to the same domain and range as the domain and range on the scatterplot, the graph is as follows:
The refined equation fits the data much more closely at the beginning, yet around the Age = 13 mark it starts to deviate again. Looking at this graph, one can come to the conclusion that it will take more than one mathematical function to graph the entirety of the data.
If one were to relate the concept of human growth with the measurable
plot(ncbirths$mage, ncbirths$weeks, xlab = "Mother's Age", ylab = "Maternity length (weeks)", main = "Maternity length based on Mother's Age")
The slope of the linear fit of the data is 1.0049. What this tells me about the water is that it is increasing at a close to constant rate – while my results were not completely accurate because the slope of the line was not one it was fairly close to the target
In the following graph, the exponential function has a very similar trend to the trend of y=2x. It is important to note that the exponential function is actually y=ax where a > 0. Using y=1x would only produce a horizontal line. Therefore the next value used was y=2x. In order to make the function fit better with the points we make transformations that slightly change the function. The first step is to lower the line so that the line can become closer to the data points. With this data set it sloa stands to reason that there are negative numbers very much possible. It would work in the exponential equation 2x-1.
The significance of her BMI is used for the estimation of weight that is associated with health and longevity. It is
For the first five data point, the value of exponential model is close to the actual value. However, the exponential model didn’t work well for the
The first quadrant of the graph was used so the shaded portion goes to the origin before it stops at the two axes.
6. Why is the black line so much more variable than the red line? What 's the difference between the data they show?
Initially, 8 pennies were added to the cup, followed by the addition of 7 pennies and 1 dime, then 4 pennies and 4 dimes, and finally 8 more pennies. There were therefore a total of 27 pennies and 5 dimes added to the cup. Table 2 demonstrates that the force (N) for dimes and pennies went up by almost 0.20 N at each interval. Therefore, the force (N) in Table 2 did not deviate much from the force (N) seen in Table 1 where all pennies were used. The reason little variation in force was seen in Table 2 was due to mostly pennies being added to the cup. Due to so many pennies being added, the dimes had little impact on the overall force (N). If roughly an equal ratio of pennies to dimes had been added to the cup, a more distinct variation between the slope’s in Figure 1 and Figure 2 would have been seen. However, the slope or the average weight of the coins, as represented in Figure 2, was 0.0249 N. The slope can be calculated by dividing the change in the force by the change in the # of pennies and dimes. The x-values represent the number of pennies and dimes, while the y-values represent force (N). The y-intercept value is equal to 0, therefore, the linear equation is y=0.0249x+0. After plotting the line on a manual curve fit, as can be seen in Figure 2, the R2 value was 0.99884. This R2 value is very close to 1, meaning that the match of the linear model to the data fits. After running a
Although laws have been implemented to fight this disease, new legislations are still been negotiated with different ways of trying to rectify the issue. Despite these rules and regulations, childhood obesity continues to plague the society. According to Hajian-Tilaki et al. (2011), the current approach in determining the presence of obesity is the body mass index (BMI). The BMI is calculated by using the height and weight to determine if an individual is overweight or obese. In the case of a child, an age and weight specific BMI is used to determine their weight status. This is required because children’s body composition varies as they get older and it also varies between boys and girls. A child with a BMI at or over the 85th percentile and below the 95th percentile for a child of the same age and sex is considered overweight. If the child has a BMI that is over the 95th percentile for a child within the same category is considered obese (Hajian-Tilaki et al., 2011). The authors also stated that males were more at risk than female in developing childhood obesity in the region of Babol. Furthermore, Hajian-Tilaki et al. mentioned a few contributing dynamics that may lead to obesity, such as genetic and metabolic factors, lack of physical activities, unhealthy eating habits, and socioeconomic standards. With all said and done, the goal of eradicating childhood obesity is still been
the range is selected for speed is the 10 times of the standard deviation of the curve at a
A tool known as BMI (body mass index) is used by medical providers to calculate an individual 's body mass index. It calculated by measuring a child’s weight and height and the found value is then compared to percentiles relative to other children of the same age and sex. For example, if a child aged anywhere from 2-19 is “more than 85% and less than 95%” they are considered overweight. (Center for Disease Control and Prevention, 2009). This tool is not a method used to diagnosis childhood obesity but it 's a valuable way to measure the prevalence of obesity worldwide.
Knowing this information, you need to first tell me, and then show this in your graph:
1. Generate a scatterplot for income ($1,000) versus credit balance ($), including the graph of the best fit line. Interpret.
To do this plot, it was took the reciprocal of everything. The reciprocal formulas used was “=1/”. It was selected the cell and typed the formula, and then selected the cell need it to do reciprocal of. It was started with B40, so it was like “=1/B40”. Since data was organized, it was used the black cross again to spread the formula around the other cells in the data set. It was repeated the same produce for I=5, 15, and 20 and for Inhibitor 2, and 3 to yield all to have the double reciprocal data. Finally, by doing these 3 graphs, can be calculated the Km and Vmax for each inhibitor concentration. To allow to do this, it was selected Chart, but now it was used Marked Scatter plots because this does not allow to connect the points. After, it was added the four inhibitor concentrations, added labels to the X and Y-axis, given a title, and selected Add Trendline. Then, it was selected “Display equation on the chart” and under Forescast was changed into 0.1 Periods in Backwards. This allowed to see where the X and Y-axis hit, and allow to determine the type of
The line of best-fit is used to find the gradient, the T2/L value, if straight or linear it shows that the relationship between the two is directly proportional. Using the original equation, you can square both sides and rearrange it to make . Then you can input the gradient value (T2/L) and work out g. , where g equals 10.13 m/s2. This value is close to the