Let's analyze the problem and solve it step by step:

(a) Choose the correct statement:

Looking at the graph, as time increases, the amount of candy in the container increases. So, the second option is correct:

• "As time increases, the amount of candy in the container increases."

Now, let’s calculate the rate of change (rate of increase). This is the slope of the graph.

The slope $m$ is calculated as: $m = \frac{\text{Change in candy (y)}}{\text{Change in time (x)}}$

From the graph:

• At $x = 0$, $y = 40$ (starting value of candy in pounds).
• At $x = 8$, $y = 200$.

$m = \frac{200 - 40}{8 - 0} = \frac{160}{8} = 20 \, \text{pounds per minute.}$

Thus, the rate of increase is 20 pounds per minute.

(b) Candy amount at $t = 0$:

From the graph, at $t = 0$, the amount of candy is clearly 40 pounds.

Final Answers:

(a) As time increases, the amount of candy in the container increases.
Rate of increase: 20 pounds per minute.

(b) At $t = 0$, the amount of candy is 40 pounds.

Would you like a detailed explanation of the calculations? Here are 5 related questions for practice:

1. How would the rate of candy increase change if the slope of the graph were steeper?
2. What does the y-intercept of the graph represent in this context?
3. If the machine stopped after 10 minutes, how much candy would be in the container?
4. What would the graph look like if the rate of increase were halved?
5. How would you calculate the total amount of candy added over a period of time?

Tip: Always remember that the slope of a graph represents the rate of change in real-world problems.