University:
Washington State University
Course:
MATH 172 | Calculus II
Academic year:

2024
Views:

30

Pages:

4
Author:

Bailey Ayala

Question 1 Which scatterplots show the following associations? (a) Little or no association: Scatterplot (1) shows no pattern, indicating little or no association. (b) Negative association: Scatterplot (4) shows a downward trend, indicating a negative association. (c) Linear association: Scatterplots (2) and (4) show consistent upward and downward patterns, respectively, indicating linear associations. (d) Moderately strong association: Scatterplot (3) shows a parabolic nature, suggesting a moderately strong association. (e) Very strong association: Scatterplots (2) and (4) show strong linear relationships, indicating very strong associations. Question 2 Which set of ordered pairs could be generated by an exponential function? Options: A: ( 0 , 0 ) , ( 1 , 1 ) , ( 2 , 8 ) , ( 3 , 27 ) (0,0),(1,1),(2,8),(3,27) B: ( 0 , 1 ) , ( 1 , 2 ) , ( 2 , 5 ) , ( 3 , 10 ) (0,1),(1,2),(2,5),(3,10) C: ( 0 , 0 ) , ( 1 , 3 ) , ( 2 , 6 ) , ( 3 , 9 ) (0,0),(1,3),(2,6),(3,9) D: ( 0 , 1 ) , ( 1 , 3 ) , ( 2 , 9 ) , ( 3 , 27 ) (0,1),(1,3),(2,9),(3,27). Solution: The general exponential form is: 𝑓 ( 𝑥 ) = 𝑎 ⋅ 𝑏 𝑥 , 𝑎 ≠ 0 , 𝑏 > 0 , 𝑏 ≠ 1. f(x)=a⋅b x ,a  =0,b>0,b  =1. Only Option D follows the form 𝑓 ( 𝑥 ) = 3 𝑥 f(x)=3 x : 𝑓 ( 0 ) = 1 , 𝑓 ( 1 ) = 3 , 𝑓 ( 2 ) = 9 , 𝑓 ( 3 ) = 27. f(0)=1,f(1)=3,f(2)=9,f(3)=27. Answer: D Question 3 (a) Make a scatterplot for the data: Heights (in.): 77 , 76 , 75 , 70 , 74 , 73 , 74 77,76,75,70,74,73,74, Weights (lb.): 230 , 220 , 212 , 190 , 201 , 245 , 260 230,220,212,190,201,245,260. Scatterplot: Horizontal axis: Heights (69–78 range). Vertical axis: Weights (180–270 range). (b) Which display is more appropriate: the table or scatterplot? The scatterplot is more appropriate, as it shows the relationship between height and weight visually. For example, a trend indicating that taller players weigh more is apparent in the scatterplot but harder to see in the table. Question 4 Describe three positive relationships in scatterplots: Strong Positive Correlation: Points form a steep, straight line slanting upward. Example: 𝑟 > 0.7 r>0.7. Moderate Positive Correlation: Points form a less steep upward trend, with some scatter. Example: 0.3 < 𝑟 < 0.7 0.3