Let me guide you through the problem step by step based on the image provided:

Part (b): Change in time ($\Delta t$)

You already answered this part correctly: $\Delta t = 10.4 - 5.6 = 4.8 \text{ hours}$

Part (c): Change in height ($\Delta h$)

The rate at which the candle burns is given as 1.8 inches per hour. Therefore, the change in height is calculated using the formula: $\Delta h = -1.8 \times \Delta t$ Since $\Delta t = 4.8$ hours: $\Delta h = -1.8 \times 4.8 = -8.64 \text{ inches}$

So, the change in height $\Delta h = -8.64$ inches.

Part (d): Height after 10.4 hours

The initial height at $t = 5.6$ hours is $h_i = 9.92$ inches (from the graph). Using the formula: $h = h_i + \Delta h$ Substitute the values: $h = 9.92 + (-8.64) = 1.28 \text{ inches}$

So, the height of the candle at 10.4 hours after it was lit is 1.28 inches.

Part (e): General formula for the candle height

The candle height decreases at a constant rate of 1.8 inches per hour. Given the height at $t = 0$ as $h_0 = 18$ inches (from the graph), the general formula for the height $h$ at any time $t$ is: $h = h_0 - 1.8 \times t$

This formula will give the height of the candle for any given $t$.

Would you like to discuss any specific part in more detail?

Here are five related questions to practice:

1. What would be the candle height at $t = 6$ hours using the general formula?
2. If the candle burns at 2 inches per hour, what would be the change in height over 5 hours?
3. How would the formula for $h(t)$ change if the initial height was 20 inches?
4. What is the time $t$ when the candle completely burns out if the height starts at 18 inches?
5. If the candle burned slower at 1 inch per hour, how long would it take to burn out?

Tip: Always track units during calculations, especially in rate problems involving time and physical dimensions!