Question

a machine at a bakery is pouring out flour. the graph shows the amount of flour (in grams) in the machine versus time (in minutes). (a) what is the amount of flour in the machine at 0 minutes? 720 grams (b) choose the statement that best describes how the time and amount of flour are related. then fill in the blank. as time increases, the amount of flour in the machine decreases. at what rate is the amount of flour decreasing? grams per minute as time increases, the amount of flour in the machine increases. at what rate is the amount of flour increasing?

Explanation:

Step1: Identify the initial and final values

At \( t = 0 \) minutes, the amount of flour is \( 720 \) grams (from part (a)). At \( t = 4 \) minutes, the amount of flour is \( 0 \) grams (from the graph, the line hits the x - axis at \( t = 4 \)).

Step2: Calculate the rate of change

The rate of change (slope) of a linear function is given by \( \frac{\text{Change in } y}{\text{Change in } x} \). Here, the change in the amount of flour (\( \Delta y \)) is \( 0 - 720=- 720 \) grams (negative because it's decreasing) and the change in time (\( \Delta x \)) is \( 4 - 0 = 4 \) minutes. The rate of decrease is the absolute value of the slope (since we are asked for the rate of decreasing). So the rate \( r=\frac{720}{4}=180 \) grams per minute.

Answer:

(a) 720 grams
(b) As time increases, the amount of flour in the machine decreases. The rate of decrease is 180 grams per minute.