Question

the number of gallons , y , sprayed from the conservation Automatic Sprinkler after X minutes can be modeled by the equation y= 2.25x + 2. The number of gallons y , sprayed from the earth Friendly Sprinkler after X minutes is modeled in the table.

Answer 1

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:

$m=\frac{y2-y1}{x2-x1}$

Take, the points:

(x1, y1) ==> (2, 8)

(x2, y2) ==> (3, 10.5)

Thus, we have:

$\begin{gathered} m=\frac{10.5-8}{3-2} \\ \\ m=\frac{2.5}{1} \\ \\ m=2.5 \end{gathered}$

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:

$\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{8.75-6.5}{3-2} \\ \\ m=\frac{2.25}{1} \\ \\ m=2.25 \end{gathered}$

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.