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Dec 03, 2024 | 416 words | 4 min read
3.2.3. Task 3
Learning Objectives
By the end of this task, you will be able to analyze and interpret bacterial
growth data, construct a mathematical model to represent the growth curve, and
validate the model using the provided dataset, ultimately demonstrating their
ability to predict bacterial growth trends over a given time period.
Introduction
Your team has a sample of an unidentified bacterial specimen, and you would like
to model its growth. You have access to a dataset where the number of bacteria
were counted every \(2\) hours over a \(36\)-hour period. You will use
the data, found in the spreadsheet ex3_team_3_teamnumber.xlsx, to
create a model of the bacterial growth.
Task Instructions
Open the answer sheet ex3_team_3_teamnumber.xlsx. Save it with
your team number replacing teamnumber in the file name.
In the Input Section of the sheet, import the time (in hours) and
bacterial count from bacterial_growth.csv
In the Calculation Section, use a formula to fill in the “\(\log_{10}\) Time”
and “\(\log_{10}\) Bacterial Count” columns. These columns will be the base \(10\)
logarithmic value of the corresponding “Time” and “Bacterial Count” columns.
In the Output Section you will create \(4\) scatter plots with axes that are
linear, semi-log x, semi-log y, and log-log. Be sure that each plot has an
appropriate title and correctly labeled axes.
Create the linear plot by using the “Time” and “Bacterial Count” columns
Create the semi-log x plot by using the “\(\log_{10}\) Time” and “Bacterial
Count” columns
Create the semi-log y plot by using the “Time” and “\(\log_{10}\) Bacterial
Count” columns
Create the log-log plot by using the “\(\log_{10}\) Time” and “\(\log_{10}\)
Bacterial Count” columns
For each plot, add a trendline that best fits the data. Display the equation
and \(R^2\) value for each trendline.
Note
While the polynomial fit will often give a high \(R^2\) value, it is prone to
over-fitting and may not be the best model of the data. Be sure that your
model actually displays polynomial behavior when using this fit.
Copy the following questions into the Output Section of the
spreadsheet and then add your answers.
What type of trendline did you use to best fit the data in that plot?
Justify your answers.
Use the model you chose in the previous question to predict the number of
bacteria present after \(19.5\)hours. Is this number consistent with
the given dataset? Why or why not?
Use the model you chose in the first question to predict the time when
there were \(20\) bacteria present. Is this number consistent with the
given dataset? Why or why not?
Print two PDF files of ex3_team_3_teamnumber.xlsx, one with values
showing
(ex3_team_3_teamnumber_values.pdf)
and the other with formulas
(ex3_team_3_teamnumber_formulas.pdf).
