I t 1 3 5 7 w 2 1 0 1 II t 1 2 3 4 w 2 3 5 8 III t 1 2 3 4 w 1 4 9 16 All are

I t 1 3 5 7 w 2 1 0 1 ii t 1 2 3 4 w 2 3 5 8 iii t 1

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I. t 1 3 5 7 w 2 1 0 -1 II. t 1 2 3 4 w 2 3 5 8 III. t 1 2 3 4 w 1 4 9 16
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All are linear. Correct! I. only. III. only. None are linear. II. and III. only. In I. the relationship is linear. In II. and III. the relationships are not linear. In both cases, the rate of change of w w is increasing. Question 4 1.67 / 1.67 pts Let s(t)=t 2 −1 s(t)=t2−1. Calculate s(a−1) s(a−1). Correct! a 2 −2a a2−2a a 2 −2 a2−2
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a 2 −a+1 a2−a+1 a 2 −2a+1 a2−2a+1 a 2 a2 Plug in t=a−1 t=a−1 and simplify: s(t)s(a−1)=t 2 −1=(a−1) 2 −1=a 2 −2a+1−1=a 2 −2a s(t)=t2−1s(a−1)=(a−1) 2−1=a2−2a+1−1=a2−2a Question 5 1.67 / 1.67 pts Calculate the average rate of change of f(t)=5t 3 −t f(t)=5t3−t on the interval [−1,1] [−1,1]. 12 12 52 −52 32 32 Correct! 4 4
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0 0 The average rate of change of f(t) f(t) over the interval [a,b] [a,b] is f(b) −f(a)b−a f(b)−f(a)b−a f(1)−f(−1)1−(−1)=4−(−4)2=82=4 f(1)−f(−1)1−(−1)=4−(−4)2=82=4 Question 6 1.66 / 1.66 pts Find the relative change of the quantity T if T changes from 0.7 to 0.05. Reminder: calculator can be used on quizzes if needed. approx -13.0 approx 0.48 approx 1.30 Correct! approx -0.93 approx -0.29 The relative change in T T is change in TT = T 1 −T 0 T 0 change in TT=T1−T0T0, where T 1 T1 is the new value of T T and T 0 T0 is the previous value of T T.
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We have Relative Change in T= 0.05−0.70.7 =≈−0.93 Relative Change in T=0.05−0.70.7=≈−0.93 Question 7 1.67 / 1.67 pts The table below shows the wind chill temperature, T, in degrees Fahrenheit when the ambient temperature is 20F, as a function of the wind speed in miles per hour (mph). Calculate the average rate of change in the wind chill temperature (in degrees F per mph) when the wind speed changes from 0 to 20 mph. The average rate of change here gives us the change in the windchill temperature for a 1 mph increase in windspeed (on average). wind (mph) 0 5 10 15 20 2 5 30 35 windchill temp (F) 20 13 9 6 4 3 1 0 4 F per mph -0.2 F per mph -2.5 F per mph -1.4 F per mph Correct! -0.8 F per mph The average rate of change (in windchill temp per mph) is the change in windchill divided by the change in windspeed: Average Rate of Change of windchill = 4−2020−0 = −1620 =−0.8 F per mph. Average Rate of Change of windchill =4−2020−0=−1620=−0.8 F per mph.
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Question 8 1.67 / 1.67 pts The table below shows y as a function of x, so that y=f(x). According to the data in the table, is the function f(x) increasing or decreasing (as x increases)? Does f(x) appear to be concave up, concave down, or linear? x 0 5 10 15 20 25 30 35 y 20 14 9 5 2 0 -1 -1.5 f(x) is decreasing linearly. f(x) is increasing and concave down. f(x) is increasing and concave up. f(x) is decreasing and concave down. Correct! f(x) is decreasing and concave up. f(x) is decreasing. Notice that the size of the decrease is getting smaller as x x gets larger. This means that f(x) f(x) is concave up. This may be more clear by looking at a plot plot of the points in the table
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Question 9 1.66 / 1.66 pts A graph of a function f(x) is shown above. On the interval [a,b], state whether f(x)f is increasing or decreasing. Also whether f(x) is concave up, concave down, or linear on the interval [a,b].
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