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).

The y axis is going from 70 to 700
The x axis is going from 0 to 9

Line on the graph:
Y: 630
X: 3
Time (minutes)
(a) At what time does the flour in the machine reach 0 grams?
[minutes
(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?
grams per minute

1 answer

To answer your questions regarding the flour machine in the bakery, let's break it down:

(a) Since we know that at time \( x = 3 \) minutes, the amount of flour \( y \) is 630 grams, we need to determine when the flour reaches 0 grams. To do this, we would typically look at the graph you described to see where it intersects the x-axis (which would indicate 0 grams of flour). However, since I don't have the visual data, I can't provide an exact time.

If you have the equation of the line, or if other points are given (such as the starting point at 0 minutes or the rate of decrease), we could use that information to calculate when it reaches 0 grams.

If we assume a linear decrease and know some additional data points, we could estimate the time to reach 0 grams from the starting point. For example, if the line starts at 700 grams and declines to 0 grams, we would look for the x-intercept.

(b) The statement that best describes the relationship is:

  • As time increases, the amount of flour in the machine decreases.

To find the rate at which the flour is decreasing, you would need to know two data points on the line. For instance, if the flour starts at 700 grams at 0 minutes and goes down to 630 grams at 3 minutes, you can find the rate like this:

  1. Calculate the change in flour: \[ \text{Change in flour} = 700 , \text{grams} - 630 , \text{grams} = 70 , \text{grams} \]
  2. Calculate the change in time: \[ \text{Change in time} = 3 , \text{minutes} - 0 , \text{minutes} = 3 , \text{minutes} \]
  3. Determine the rate of decrease: \[ \text{Rate of decrease} = \frac{\text{Change in flour}}{\text{Change in time}} = \frac{70 , \text{grams}}{3 , \text{minutes}} \approx 23.33 , \text{grams per minute} \]

Thus, if these specific points are correct, the rate at which the amount of flour is decreasing is approximately 23.33 grams per minute.

If you provide different starting points or confirm the data points on the graph, we could find the exact rate and time to reach 0 grams.