210
Chapter 2 Graphs and Functions
63. (a) First find the slope using the points (0, 22036) and (4, 24525). 24525 22036 2489 m 622.25 40 4 The y-intercept is (0, 22036), so the equation of the line is y 622.25x 22, 036. 60, 000
(c) 76.9 x
60, 000 x x 780 76.9 According to the model, the galaxy Hydra is approximately 780 megaparsecs away. The slope of the line indicates that the average tuition increase is about $622 per
(d) A A
year from 2009 through 2013. (b) The year 2012 corresponds to x = 3. y 622.25 3 22, 036 23, 902.75 According to the model, average tuition and fees were $23,903 in 2012. This is $443 more than the actual amount
9.5 1011 m 9.5 1011
10
1.235 10
76.9
9
12.35 10
Using m = 76.9, we estimate that the age of the universe is approximately 12.35 billion years. (e)
A
9.5 1011
1.9 10
10 or 19 10
9
50 9.5 10 11 A 9.5 109 100 The range for the age of the universe is between 9.5 billion and 19 billion years.
$23,460. (c) Using the linear regression feature, the equation of the line of best fit is y 653x 21, 634.
65. (a) The ordered pairs are (0, 32) and (100, 212). 212 – 32 180 9 The slope is m . 100 – 0 100 5 Use ( x1 , y1 ) (0, 32) and m 59 in the point-slope form. y – y1 m( x – x1 ) y – 32 9 (5x – 0)
64. (a) See the graph in the answer to part (b).There appears to be a linear relationship between the data. The farther the galaxy is from Earth, the faster it is receding. (b) Using the points (520, 40,000) and (0, 0), we obtain 40,000 – 0 40,000 m 76.9. 520 – 0 520 The equation of the line through these two points is y = 76.9x.
y – 32
9
x
5
y
5
(b)
(c)
9
x 32 F
9
C5 32
F 9C 32 5 5F 9 C 32 5F 9C 160 9C 5F – 160 9C 5(F – 32) C 5 ( F –9 32) F C F 5 (F –9 32) 9F 5(F – 32) 9F 5F – 160 4F –160 F – 40 F = C when F is – 40º.