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University of Negros Occidental-Recoletos

This document presents an activity on curve fitting using data on bacterial growth over time. The data was fitted to linear, exponential, and parabolic curves using a scientific calculator and Excel. The exponential curve provided the best fit with an R-squared value closest to 1. Both the calculator and Excel predicted the bacteria amount after 40 days to be approximately 503 million and 501 million respectively using the exponential equation. Therefore, the conclusion is that the exponential equation best models the bacterial growth data.

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Allen Castor
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70 views4 pages

University of Negros Occidental-Recoletos

This document presents an activity on curve fitting using data on bacterial growth over time. The data was fitted to linear, exponential, and parabolic curves using a scientific calculator and Excel. The exponential curve provided the best fit with an R-squared value closest to 1. Both the calculator and Excel predicted the bacteria amount after 40 days to be approximately 503 million and 501 million respectively using the exponential equation. Therefore, the conclusion is that the exponential equation best models the bacterial growth data.

Uploaded by

Allen Castor
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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UNIVERSITY OF NEGROS OCCIDENTAL-RECOLETOS

COLLEGE OF ENGINEERING

MELAB142P

CURVE FITTING
ACTIVITY NO. 1

Allen S. Castor

BSME – IV

Engr. Glenn Amantillo

Instructor

June 27, 2017


Objective: To fit the curve using scientific calculator and excel.

Data:

Table 1: Data that represents the bacterial growth in a liquid culture over a number of
days

x
0 4 8 12 16 20
(Day)
y
67 84 98 125 149 185
(Amount x10^6)

Results:

Figure 1: Results of the bacterial growth in a liquid culture over a number of days using
an excel

200
180 185

160
149
140
Amount (x10^6)

120 125
y = 5.8x + 60 Series1
100 98 R² = 0.9755 Linear
80 84
Exponential
67
60
y = 67.306e0.0503x y = 0.1507x2 + 2.7866x + 68.036 Parabolic
40 R² = 0.9979 R² = 0.9979
20
0
0 5 10 15 20 25
Day/s
Calculations: Results of bacterial growth in a liquid culture over a number of days by
using a Fx-82ES scientific calculator

Linear (A + Bx):

A = 60 ; B = 5.8 ; R = 0.9876620818

A + Bx  60 + 5.8x

y = 5.8x + 60

Exponential (AeBx):

A = 67.30603643 ; B = 0.05029322006 ; R = 0.9989323106

AeBx  67.30603643e0.05029322006x

y = 67.30603643e0.05029322006x

Parabolic (A + Bx + Cx2):

A = 68.03571429 ; B = 2.786607143 ; C = 0.1506696429

A + Bx + Cx2  68.03571429 + 2.786607143x + 0.1506696429x2

y = 68.03571429 + 2.786607143x + 0.1506696429x2

Table 2: Using the exponential equation to be substituted using both results in a


calculator and an excel

Using a exponential equation Using an exponential equation


(calculator) (excel)

y = 67.30603643e0.05029322006x y = 67.306e0.0502x
y = 67.30603643e0.05029322006(40) y = 67.306e0.0502(40)
y = 503.1954833 y = 501.3223893

503.1954833x106 501.3223893x106
(Amount of bacteria after 40 (Amount of bacteria after 40
days) days)
Discussion:

Results showed that the exponential equation was the best equation to the data
trend based on the value of the correlation coefficient r that is closest to +1.

Results in excel showed that the correlation coefficient r of both parabolic and
exponential in finding the square-root was the same, but in the calculator fx-82ES, it
didn’t have the value for correlation coefficient r that can be compared.

The variable x of exponential equations of both excel and calculator were


substituted to predict the amount of bacteria after 40 days.

Conclusion:

The exponential equation is the best equation using both excel and calculator.
The amount of bacteria predicted after 40 days was 503.1954833x106 in calculator and
501.3223893x106 in excel.

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