The given table models the number of gallons y , sprayed from the earth Friendly Sprinkler after X minutes.
x y
2 8
3 10.5
4 13
Where x represents the number of minutes and y represents the number of gallons.
The rate of change can also be called the slope.
To find the sprinkler system with the greatest rate of change, apply the slope formula:
Take, the points:
(x1, y1) ==> (2, 8)
(x2, y2) ==> (3, 10.5)
Thus, we have:
The rate of change for the earth friendly modelled sprinkler is 2.5 gallons per minute
For the Automatic sprinkler, we have the equation:
y = 2.25x + 2
Let's find the values of x and y.
When x = 2
y = 2.25(2) + 2 = 4.5 + 2 = 6.5
When x =2, y = 6.5
When x = 3
y = 2.25(3) + 2 = 6.75 + 2 = 8.75
To find rate of change take the points:
(x1, y1) ==> (2, 6.5)
(x2, y2) ==> (3, 8.75)
Thus, we have the rate of change:
The rate of change for the Automatic sprinkler is 2.25
The sprinkler system with the greatest rate of change is the earth friendly sprinkler at 2.5 gallons per minute.
ANSWER:
B. Earth Friendly Sprinkler has the greatest rate of change, at 2.5 gallons per minute.