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Key Topics
Requirement
1). Using the model provided above use Excel to work out the number of bacteria for 25 consecutive days.
? Provide two columns of your data and represent that information with a scatter diagram.
? Add a trend line.
? Please comment on any issues you may have encountered with these data.
2). Now, take simply the first digit (D) of the bacteria population you have and measure the frequency of every first digit. (You are encouraged to investigate and experiment with the “countif ” function in Excel.)
? Plot a bar chart with the frequency of each digit.
? What do you observe?
? Is this in line with Benford’s Law?
? Elaborate on your findings.
3). Considering that the population growth of bacteria follows an exponential function,“linearize” your exponential function using algebra and provide a scatter diagram with its associated trend line.
? Using Excel, provide the equation of your new line.
? Using algebra, provide the equation of your new line
? Compare your results to part 4 and comment.
? Establish the relationship between the linearized form and the original exponential function.
4). Revisit Benford’s Law using the linearized form and repeat the process in part (3) for your new
data. What do you observe?
Solution
Computing Assignment
Model
Experimental data of heat capacities of chemicals or bacteria growth tend to obey Benford’s Law, which states that given some numerical data the proportion of numbers starting with digit D is approximate: P(D) = log??(1 + ) where P(D) is the proportion of a number starting with digit D. (For example, given 43.38, D=4.)
Putting to test Benford’s Law, let’s use the following exponential growth model used for the growth of bacteria in an experiment sample: N = 2e²? ? ¹
where N is the population number of bacteria at time t, measured in days.
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Questions;
1). Using the model provided above use Excel to work out the number of bacteria for 25 consecutive days.
Provide two columns of your data and represent that information with a scatter diagram.
Add a trend line.
Please comment on any issues you may have encountered with these data.
2). Now, take simply the first digit (D) of the bacteria population you have and measure the frequency of every first digit. (You are encouraged to investigate and experiment with the “countif ” function in Excel.)
Plot a bar chart with the frequency of each digit.
What do you observe?
Is this in line with Benford’s Law?
Elaborate on your findings.
3). Considering that the population growth of bacteria follows an exponential function,“linearize” your exponential function using algebra and provide a scatter diagram with its associated trend line.
Using Excel, provide the equation of your new line.
Using algebra, provide the equation of your new line
Compare your results to part 2 and comment.
Establish the relationship between the linearized form and the original exponential function.
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Place Your Order4). Revisit Benford’s Law using the linearized form and repeat the process in part (2) for your new data. What do you observe?
Special instructions: All Excel Spreadsheet needs to be emailed to me.
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