I am not too sure if I did this question correct. Thanks in advanced!
Data table:
Time after Consumption (min): 30 60 90 120 150 180
Amount of Codeine in Blood (mg): 27.0 23.5 21.2 18.7 16.6 14.5
1.) create a scatter plot of the data and determine a suitable equation to model the amount of codeine in the bloodstream t min after taking the pill. Justify your choice of models.
This is what I did: I labelled the x-axis as Time (min) and the y-axis as Amount of Codeine (mg) and then I plotted each of the points.
After that I used the formula A=Pe^kt and got the equation A=31.0213e^-0.00463t. Would this equation be correct? Also, what does the question mean by "Justify your choice of models"
Did you end up solving this question?
Your approach in creating the scatter plot and labeling the axes correctly is a good start. However, the equation you provided, A=31.0213e^-0.00463t, is not appropriate for modeling the data in this case.
To determine a suitable equation to model the amount of codeine in the bloodstream over time, you need to consider the shape of the data. Looking at the scatter plot, you can observe that the relationship between time and the amount of codeine in the bloodstream appears to be decreasing steadily. It does not appear to be an exponential relationship, as the equation you used implies.
One model that might be suitable for this data is a linear regression. This model assumes that there is a linear relationship between the independent variable (time) and the dependent variable (amount of codeine in the bloodstream). To justify your choice of this model, you can explain how the data aligns with the assumptions of a linear relationship.
In this case, the data points seem to generally follow a straight line pattern when plotted on the scatter plot. Additionally, the relationship between time and the amount of codeine in the bloodstream is expected to be consistent, without any significant non-linear changes or exponential growth/decay.
To fit a linear regression model to the data, you would be looking for an equation of the form:
Amount of Codeine = a * Time + b
By using statistical software or methods, you can calculate the best-fit values of the coefficients a and b for the equation. These values will represent the slope and intercept of the line, respectively.
Once you have the equation, you can evaluate how well it fits the data by examining metrics such as the coefficient of determination (R-squared) or looking at the residuals. A higher R-squared value indicates a better fit to the data.
Therefore, in summary, the equation A=31.0213e^-0.00463t is not suitable for modeling the data. Instead, a linear regression model, which assumes a linear relationship between time and the amount of codeine in the bloodstream, may be appropriate. Justify this choice by explaining how the data aligns with the assumptions of a linear relationship.