4. Match each of the slope fields below (SF1-SF4) with a differential equation (A-D). Try to dothis without plotting slope fields in Desmos. Give a one sentence explanation for why youchoose to pair each slope field with a particular differential equation.Slope fields:4-4-10SF110-10SF2104SF34SF4| |2| |0-2-4-10-50510-10-50510Differential equations:dyB.A.= x - ydx12dydx33C.dydxD.=2-y33dy= xdx

A. For dxdy+p(x)y=f(x), the solution isy=e−∫p(x) dx(e∫p(x) dxf(x)…

Answered: 4. Match each of the slope fields below…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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19.
1. The average per-person annual consumption of sports drinks in the U.S. is shown in the table for various years. Let C be the average per-person annual consumption (in gallons per person) of sports drinks at t years since 2000. a) Use your GC to find the regression equation to model the data. b) Rewrite your equation using function notation, C(t). Year 2002 2003 2004 2005 2006 d) What is the slope? What does it mean in this application? Annual Consumption (gallons per person) 2.7 3.0 3.4 4.1 4.5 c) Use your equation to predict the average annual per-person sports drink consumption in 2012.
The annual expenditure for cell phones varies by the age of an individual. The average annual expenditure E(a) (in $) for individuals of age a (in years) is given below:a: 20, 30, 40, 50, 60, 70E(a): 502, 658, 649, 627, 476, 2131. Use quadratic regression to find the model that best represents the data.2. At what age is the yearly expenditure for cell phones the greatest? Round the answer to the nearest year. YOU MUST SHOW THE WORK FOR THIS PART!
Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X1), the annual income of the family (X2), and the number of times the family went out on an outing in the last year (X3). She collects data from 196 families and estimates the following regression: Y=120.45+1.54X1+2.12X2+2.12X3. Suppose β1, β2, β3, denote the population slope coefficients of X1, X2, and X3, respectively. The researcher wants to check if neither X1 nor X2 have a significant effect on Y or at least one of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic for the test with the two restrictions (H0: β1=0, β2=0 vs. H1: β1≠0 and/or β2≠0) to be 3.00. The p-value for the test will be enter your response here?
Create a quadratic model for the data shown in the table 1 -1 X -1 -1 y Oy=0.85r² +0.11 - 1.78 y = 0.98x² -0.74 - 0.82 y = 0.112²1.78x +.9998 X y = -0.85x² -0.11x +1.78 2 2 5 20
A study investigating the relationship between a country's annual gross domestic product x (in trillions of dollars) and carbon dioxide emissions y(in millions of metric tons) yielded r = 0.87, se = 141.9 , and the regression equation y-hat = 199.5x + 56.0. For each additional trillion dollars in %3D gross domestic product, carbon dioxide emissions increases by about 0.87 million metric tons, on average increases by about 199.5 million metric tons, on average changes by an amount that cannot be determined from the information given O increases by about 141.9 million metric tons, on average increases by about 56.0 million metric tons, on average
Given are five observations for two variables, and y. a. Choose the correct scatter diagram for these data: A. C. D 60 50 40 30- 20 -10- 60 50 40 -30 20 10- 10 10 20 20 30 30 40 40 50 50 60 x 60 x B. D. 60 50 40 30 20 10- 60 50 40 30- 20 10- 10 10 20 20 30 30 40 40 50 50 60 x 60 x 5 15 8 23 19 Xi Yi 55 40 50 15 25 b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a negative linear relationship between x and y. and y by drawing a straight line through the data. c. Try to approximate the relationship between Many different straight lines can be drawn ✔ to provide a linear approximation of the relationship between x and y.
Assume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8 A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?
Find the second derivative of the function. s = + 9t + 5 5t3 - 2 dt2 10 ds = 20t3 + 18 dr? O ds = 5t4 - 2 10 dr? 12 O as = 20t5 + 18 30 dr2

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