MATH-105-Exam

MATH-105-Exam-1-Collaborati x + A < → C O d2.iup.edu/content/enforced1/2961456-12415.202040/MATH-105-Exam-1-Collaborative.pdf?_&d21SessionVal=DQCUFLRPJP2jHZsLmftY9Nblb an additional 15 points; Total points = 15 + 85= 100 points. 1. California Wildfires. Each dry season seems to beget California forest fires. By reading the news, we have the general impression that severity of the forest fires are worsening. In this problem, we use data from the last 33 years to quantitatively describe how the fires are worsening. See Figure 1. Obviously, the severity of the fire season fluctuates: in some Scatterplot 3 *E Y: C1:C34 2200000 2000000 1800000 1600000 1400000 1200000 1000000 800000 600000 400000 200000 0 -200000 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 Figure 1: The number of acres on fire by year. years the fire season is manageable and in other years the season is quite severe. Here, a line has been fit to the data by a technique called linear regression (you may encounter this technique in a statistics course). Software has told us that the red line, the line of best fit, is given as y = 24734.x – 48902819 • Questions are on next page. • Source: https://www.fire.ca.gov/stats-events/ • To see the original data, view Perusall > Exam 1 Supplementary Materials. PAGE 1 OF 5 POINTS: -/0 MATH-105-Exam-1-Collaborati X + + → C A d2l.iup.edu/content/enforced1/2961456-12415.202040/MATH-105-Exam-1-Collaborative.pdf?_&d2lSessionVal=DQCUFLRPJP2jHZsLmftY9Nblb 0 : MATH-105-Exam-1-Collaborative.pdf 2 / 5 ; (a) (5 points) What are more appropriate variable symbols than x and y? (b) (5 points) What is the independent variable? What is the dependent variable? (c) (5 points) Rewrite the equation of the line using the variables in part (a). (d) (5 points) What are the units of y? Units of x? (e) (5 points) What are units of the slope? Write a sentence describing the meaning of the slope. (f) (5 In a sentence, what is your response (using numbers) to the “How are California fires worsening each year?”. + (g) (5 points) By using the fit (red) line, what is the predicted number of acreage on fire in the year 2018? By visually inspecting the graph, this value is not close to the actual acreage in 2018. In a sentence, how do you make sense of the discrepancy? – MATH-105-Exam-1-Collaborati X + + → C d2.iup.edu/content/enforced1/2961456-12415.202040/MATH-105-Exam-1-Collaborative.pdf?_&d21SessionVal=DQCUFLRPJP2jHZsLmftY9Nblb O MATH-105-Exam-1-Collaborative.pdf 3 / 5 2. COVID-19 Transmission. As COVID-19 spreads, researchers (in Source A) have found a linear relationship between the growth rate ratio (GR) and mobility ratio (MR). Here the growth rate ratio may be thought of in the following manner*: GR = average number of cases in last three days average number of cases in last seven days * The actual calculation is slightly more complicated, but the above calculation represents the main idea. The following list breaks the growth rate ratio into three cases: = • GR 1: No increase in rate of cases. The average number of cases over the last three days is the same as the last seven days. • GR > 1: An increase in rate of cases. The average number of cases over the last three days is more than the average over the last seven days. • GR< 1: A decrease in rate of cases. The average number of cases over the last three days is less than the average over the last seven days. The mobility ratio is given as the following ratio: MR the sum of incoming and outgoing trips within a given county on a given day the sum of incoming and outgoing trips within a given county on a baseline day The following list gives two examples of the mobility ratio: • MR= 0: No trips were made. Everyone is staying home. • MR=.5: Half of the usual number of trips were made. The data for Pittsburgh was not listed in Source A, so we will assume Pittsburgh’s data is the same as Philadelphia’s. The linear relationship is given below, GR= .33MR+.84 + • Questions are on next page. • Source A: Association between mobility patterns and COVID-19 transmission in the USA: a mathematical modelling study • Source B: Google Mobility Reports – MATH-105-Exam-1-Collaborati x + A < → C d2.iup.edu/content/enforced1/2961456-12415.202040/MATH-105-Exam-1-Collaborative.pdf?_&d21SessionVal=DQCUFLRPJP2jHZsLmftY9Nblb O MATH 105 EXAM 1 (COLLABORATIVE) (a) (5 points) Assume MR= 0. What is GR? (b) (5 points) Using part (a), write a sentence describing what can be said about the spread of COVID-19 in Pittsburgh. (c) (5 points) Assume MR=1. What is GR? (d) (5 points) Using part (c), write a sentence describing what can be said about the spread of COVID-19 in Pittsburgh. (e) (5 points) By tracking the position of Android phones, Google has obtained data of user’s mobility patterns. In Allegheny County surrounding Pittsburgh, Google’s data over the time period Jul. 31 – Sep. 11 is presented in Figure 2. The categories in Google’s data do ot exactly correspond to the definition of mobility ratio Source A, but we will focus on the Transit Station and Workplace categories to produce an estimate for MR: each category is near -40%, which equates to MR= .6. Is MR= .6 effective at controlling the spread of COVID-19 in Pittsburgh? MATH-105-Exam-1-Collaborati x + A < С d2l.iup.edu/content/enforced1/2961456-12415.202040/MATH-105-Exam-1-Collaborative.pdf?_&d2|SessionVal=DQCUFLRPJP2jHZsLmftY9Nblb O MATH 105 EXAM 1 (COLLABORATIVE) Allegheny County Retail & recreation Grocery & pharmacy Parks -20% compared to baseline -7% compared to baseline +85% compared to baseline +80% +80% +80% +40% Baseline +40% +40% Baseline ما را با ما با ما ت Baseline -40% -40% 40% -80% Fri, Jul 31 -80% Fri, Jul 31 Fri, Aug 21 Fri Sep 11 Fri, Aug 21 Fri Sep 11 -80% Fri, Jul 31 Fri, Aug 21 Fri Sep 11 Transit stations Workplaces Residential -37% compared to baseline -42% compared to baseline +11% compared to baseline +80% +80% +80% +40% Baseline +40% Baseline +40% Baseline -40% -40% ry 40% -80% Fri, Jul 31 Fri, Aug 21 Fri, Sep 11 -80% Fri, Jul 31 Fri, Aug 21 Fri, Sep 11 -80% Fri, Jul 31 Fri, Aug 21 Fri Sep 11 Figure 2: Google’s mobility data over July 31 – September 11, 2020. 3. Using the given graph of h(x), Find the the following quantities: (a) (3 points) h(1) h(2) 2 (b) (3 points) h(0) (c) (4 points) Domain of h х (d) (4 points) Range of h -2 2 (e) (3 points) The x-intercept(s) (f) (3 points) The y-intercept -2 4. (5 points) Let f(x) = 3×2 – 4x. Find 2f (6x)
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