1 The graph shows the depth of water W in a reservoir over a

1. The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. What was the average rate of change of W between x = 0 and x = 100?  (Assume that the points lie on the grid lines.)

_______ft/day

2. The graph gives the number of farms in the United States from 1850 to 2000.

(a) Estimate the average rate of change in the number of farms between 1880 and 1900 and between 1940 and 2000. (Round your answers to the nearest whole number).

1880 and 1900 _____ farms per year

1940 and 2000 _____ farms per year  

(b) In which decade did the number of farms experience the greatest average rate of decline?

a) 1870 - 1880
b) 1910 - 1920
c) 1940 - 1950
d) 1950 - 1960
e) 1960 - 1970

Solution

1. average rate of change of W between x = 0 and x = 100

x = 0 ; W =100

x = 100 ; W =150

Average = ( 150 -100)/(100 -0) = 50/100 = 0.5

2.

a) average rate of change in the number of farms between 1880 and 1900

From graph 1880 ----2500 ; 1900 ----4500

average rate of change in the number of farms between 1880 and 1900 = ( 4500 - 2500)/(1900 -1880)

= 2000/20 = 100 per year

and between 1940 and 2000

From the graph: 1940(x) ----6000(y) ; 2000(x) ----2000(y)

Average rate of change = ( 6000 - 2000)/( 1940 -2000)

= 4000/60

=200/3 = 66.67 = 67 per year

b) In the year 1950 -1960 max. fall in no. of farms

So, greatest rate of decline : 1950 -1960

Option d)