Creating Functions and Graphs
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The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002.
Heart Disease: Year:(1985) 771169 Year:(1990) 720058 Year:(1995) 737563 Year:(2002) 696,947
Cancer: Year:(1985) 461563 Year:(1990) 505322 Year:(1995) 538445 Year:(2002) 557,271
a. Plot this data for each disease as points in a rectangular coordinate system.
b. Using a smooth line, connect your data points for each disease.
c. On a separate graph, plot only the years 1985 and 2002 and connect the points with a straight line.
d. Calculate the slope of each line.
e. Write the equation of each line in the slope-intercept form.
f. Using the equations of each line, make a reasonable prediction as to the number of deaths we might expect in 2005 due to each of these medical conditions.
1. Please include a response to this two part follow-up question with your submission.
a. Can the graphs that you constructed be classified as functions? Explain.
b. Why is it reasonable that negative numbers are excluded from both the domain and the range of each of the disease graphs? What would the real-world implications be if these numbers were actually part of the domain and/or range?
Assignment 2:
In the real world, what might be a situation where it is preferable for the data to form a relation but not a function?
There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points:
Fahrenheit Celsius
Freezing point of water (Fahrenheit) 32 (Celsius) 0
Boiling point of water (Fahrenheit)212 (Celsius) 100
1. Find the linear equation that expresses temperature in degrees Fahrenheit as a function of temperature in degrees Celsius.
2. Find the linear equation that expresses temperature in degrees Celsius as a function of temperature in degrees Fahrenheit.
3. How do the graphs of these two functions differ?
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Solution Summary
This Solution contains over 600 words and calculations to aid you in understanding the Solution to these questions.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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