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l 130 CHAPTER 2 Functions 27. at) = 3; I t=a,t=rt+h 28. to): x/i; t=a,t=a+h 29—30 I A linear function is given. (:1) Find the average rate of change of the function between
at = a and x = a + h. (b) Show that the average rate of change is the same as the
slope of the line. 29. f(x) = %x + 3 30. g(x) = 44x + 2 Applications 31. Changing Water Levels The graph shows the depth
of water W in a reservoir. over a oneyear period, as a
function of the number of days x since the beginning of
the year. (a) Determine the intervals on which the function W is
increasing and on which it is decreasing. (b) What was the average rate of change of Wbetween
x = 100 andx = 200? W (ft)
100 75
50
25 100 200 300 x(days) 32. Population Growth and Decline The graph shows the
population P in a small industrial city from 1950 to 2000.
The variable :5 represents the number of years since 1950. (3) Determine the intervals on which the function P is
increasing and on which it is decreasing. (b) What was the average rate of change of P between
x = 20 and x = 40‘? (c) Interpret the value of the average rate of change that
you found in part (b). _ P (thousands)
50
40 30
20 10 10 20 30 40 50x(‘years)l K 33. Population Growth and Decline The table gives the
population in a small coastal community for the period
19972006. Figures shown are for January 1 in each year, (a) What was the average rate of change of population
between 1998 and 2001‘? (in) What was the average rate of change of population
between 2002 and 2004‘? (c) For what period of time was the population increasing? '
(d) For what period of time was the population decreasing? ' Popuiation 34. Running Speed A man is running around a circular tracksE 200 m in circumference. An observer uses a stopwatch to " record the runner’s time at the end of each lap, obtaining the
data in the following table. (a) What was the man’s average speed (rate) between 68
and 152 s? (c) Calculate the man’s speed for each lap. Is he slowing
down, speeding up, or neither? 200 32 35. CD Player Sales The table shows the number of CDP
ers sold in a small electronics store in the years 1993400 (a) What was the average rate of change of sales haw“
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 Fall '08
 Drucker,T

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