Question

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

Explanation:

Step1: Solve part (a)

To find the amount of candy at 0 minutes, we look at the y - intercept of the graph. The y - intercept is the value of the amount of candy when time \( t = 0 \). From the graph, when \( t=0 \), the amount of candy is 60 pounds.

Step2: Analyze the relationship for part (b)

Looking at the graph, as time (x - axis) increases, the amount of candy (y - axis) increases because the line has a positive slope. To find the rate of increase, we can calculate the slope. Let's assume two points on the line. From the graph, when \( t = 0 \), \( y=60 \) and when \( t = 1 \), let's say \( y = 120 \) (we can estimate from the graph's steepness, the slope \( m=\frac{y_2 - y_1}{t_2 - t_1}\). If we take \( (0,60) \) and \( (1,120) \), then \( m=\frac{120 - 60}{1 - 0}=60 \) pounds per minute.

Answer:

(a) 60
(b) As time increases, the amount of candy in the container increases. The rate of increase is 60 pounds per minute.