Unit 3 Project
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Brigham Young University, Idaho *
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Course
110
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Mathematics
Date
Feb 20, 2024
Type
docx
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Math 110X – Unit 3 Project I certify that I did not communicate about any aspect of this project with any living human being (this includes using the internet) other than my instructor once I began the project
. The only resources I used were my Math 110X notes and a blank
spreadsheet program such as Excel (you are not allowed to use any saved Excel files). Signature: _____________________________ Print Name Here: ________________________ Instructions: Show all of your work for each problem. For some problems, the work will be done
on a spreadsheet. Please clearly indicate where your answer(s) can be found and show (possibly with labels or highlighting) your processes for obtaining the answers on the spreadsheet and upload the spreadsheet to I-Learn. You will have one Excel file with each question on a separate tab of the file. Be sure to label each tab as question 1, question 2, etc. Be sure to answer carefully
and clearly.
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1.
The following data represents the number of operating temples of the Church of Jesus Christ of Latter-day Saints.
Year Number of Operating Temples 1830 0 1880 1 1930 7 1980 19 1995 47 2000 102 2017 155 Rexburg, Idaho Temple
a.
(2 points) What type of function best describes this data set? Explain your reasoning. This would be an exponential function. There can never be less than 0 temples so there is a horizontal asymptote. The data also starts off increasing slowly then increasing fast.
b.
(8 points) Find the regression model of the data. You must find the regression function yourself using matrices. You can check your answer using the “trendline” feature of the spreadsheet, but you will not get credit for the correct answer unless you show all of the matrices you used to obtain the answer. Regression Equation: y = 9.658e-30*e^(x*0.035525)
c.
(2 points) If the number of temples operating continues this trend, how many temples will be operating by the year 2045? Show all of your work. 9.658e-30*e^(2045*0.035525) =
See highlighted in yellow on excel.
d.
(2 points) Is your answer to part c reasonable? Explain your reasoning. No, there is more temples in operation currently than what would be predicted in 2045. There is different growth patterns for temples to be built for different prophets and revelation they receive. Such us the extreme increase during the Hinkley temples. There is no equation that
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would fit the revelation of God. All temples will be built according to when God deems is necessary. e.
(4 points) What type of function would better model the growth of operating temples? Explain your reasoning. I think logistics would be a better function. There is a rapid increase of temples that are built as the church was growing fast. As we come closer to the second day and as the church growth slows down the number of temples being built will slow down.
2.
In 1935 Charles Richter defined the magnitude of an earthquake to be 𝑀𝑀 = log(𝐼𝐼) − log (𝐼𝐼
𝑜𝑜
)
, where 𝑀𝑀
is the magnitude of the earthquake, 𝐼𝐼
is the intensity of the earthquake, and
𝐼𝐼
𝑜𝑜
is the intensity of a standard earthquake or benchmark earthquake. a.
(2 points) Write the formula for the magnitude of an earthquake as a single logarithmic function. Y = log(a) + log(x) - b
b.
(4 points) The following data is the intensity of an earthquake as a multiple of the benchmark earthquake and the corresponding magnitude of the earthquake (e.g., 𝐼𝐼 = 4𝐼𝐼
𝑜𝑜
means that the intensity was four times the intensity of the benchmark
earthquake). Input the data into Excel and use Excel to find the equation of the data (you may use the Trendline feature in Excel). 𝐼𝐼
as a multiple of 𝐼𝐼
𝑜𝑜
1.5 5 10 57.5 120 178.85 1250.2 25431 50000 𝑀𝑀
on the Richter Scale 0.176091 0.69897 1 1.759668 2.079181 2.252368 3.096979 4.405363 4.69897 Equation: y=log(1.022513)+log(x)-0.025813
c.
(2 points) Compare the equations in part a and part b. Are they the same? Explain your reasoning. If they are different, give possible reasons why.
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Equations are the same, I am not sure how I figured out how to solve. d.
(2 points) If the intensity of an earthquake is 80000 times the benchmark earthquake, what is the magnitude of the earthquake? Show all of your work. Y=log(1.022513)+log(x)-0.025813 = 4.886946
See highlighted in excel
e.
(4 points) One of the largest recorded earthquakes in history occurred in Columbia on
January 31, 1906. This earthquake had a magnitude of 8.6
on the Richter scale. What was the intensity of the earthquake as a multiple of a benchmark earthquake? Show all of your work. 8.6=log(1.022513)+log(x)-0.025813
8.6=0.009669+log(x)-0.025813
8.6-0.009669+0.025813=log(x)
8.616144=log(x)
10^8.616144=10^log(x)
10^8.616144=x
X=
413184479.789
f.
(2 points) On December 17, 2016 an earthquake with an intensity of .199526 of the Columbian earthquake hit Papua New Guinea. What was the magnitude of the 2016 earthquake? Show all of your work. 3.
Upload your neat, organized, and labeled spreadsheet. 4.
Upload a single PDF of this sheet with your written work.