Question

at a candy factory, a machine is putting candy into a container. the graph shows the amount of candy (in pounds) in the container
(a) what is the amount of candy in the container at 0 minutes?
(square) pounds
(b) choose the statement that best describes how the time and amount of candy are related. then fill in the blank.
(\bigcirc) as time increases, the amount of candy in the container decreases.
at what rate is the amount of candy decreasing?
(square) pounds per minute
(\bigcirc) as time increases, the amount of candy in the container increases.
at what rate is the amount of candy increasing?
(square) pounds per minute

Explanation:

Step1: Analyze part (a)

To find the amount of candy at 0 minutes, we look at the y - intercept of the graph. The graph starts at (0, 30) (assuming the y - axis at x = 0 has a value of 30 pounds). So the amount of candy at 0 minutes is 30 pounds.

Step2: Analyze part (b)

Looking at the graph, as time (x - value) increases, the amount of candy (y - value) decreases (since the line has a negative slope). To find the rate of decrease, we can calculate the slope. Let's take two points. At x = 0, y = 30; let's assume another point, say when x = 10 minutes (we can estimate from the graph, but since the line is linear, the slope is constant). Wait, actually, from the graph, if we look at the change in y over change in x. Let's say when x = 0, y = 30 and when x = some time, y decreases. Wait, maybe the graph has a slope. Let's assume the graph goes from (0, 30) to (10, 10) (just an example, but actually, from the graph, the rate of change: the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). If at x = 0, y = 30 and at x = 1 minute, let's see, the line is decreasing. Wait, maybe the correct rate: let's check the graph. The y - axis is amount of candy (pounds) and x - axis is time (minutes). The line starts at (0, 30) and goes down. So the slope is (y2 - y1)/(x2 - x1). Let's take two points: (0, 30) and (10, 10) (not sure, but maybe the rate is 2 pounds per minute? Wait, no, maybe I made a mistake. Wait, the problem: at a candy factory, a machine is putting candy into a container? Wait, no, maybe the machine is emptying? Wait, the graph shows amount of candy decreasing? Wait, no, the problem says "a machine is putting candy into a container", but the graph is decreasing. Maybe it's a typo, but according to the graph, as time increases, amount of candy decreases. So the statement is "As time increases, the amount of candy in the container decreases." Then the rate of decrease: let's calculate the slope. Let's take (0, 30) and (15, 0) (if the line goes to 0 at 15 minutes). Then slope is (0 - 30)/(15 - 0)= - 2. So the rate of decrease is 2 pounds per minute.

But let's focus on part (a) first. At 0 minutes, the amount of candy is the y - intercept, which is 30 pounds.

Answer:

(a) 30 pounds; (b) As time increases, the amount of candy in the container decreases. At what rate is the amount of candy decreasing? 2 pounds per minute (assuming the graph has a slope of - 2, but the key for part (a) is 30 pounds)