Question

in lesson 1, you engaged in an important way of thinking when you reasoned and visualized how quantities that vary in value in the candle - burning situation changed together. in the questions above, we asked you to engage in another essential way of thinking that will extend to higher - level mathematics. note that $delta y=mcdotdelta x$ is another way to express the relationship $\frac{delta y}{delta x}=m$. this form emphasizes that $delta y$ is always $m$ times as large as $delta x$ when $x$ and $y$ vary together. note that we can also write this as follows: $delta y = mcdotdelta x$, $y_2 - y_1=mcdot(x_2 - x_1)$. the way of thinking you engaged in occurred when you were using your meanings for constant rate of change to reason about linear relationships. example 4: a burning candle - extended a candle burns at a constant rate of 1.8 inches per hour. 5.6 hours after being lit, the candle is 9.92 inches tall. the candle burns continuously until completely consumed. - let $h$ represent the candles height (in inches). - let $t$ represent the elapsed time (in hours) since the candle was lit. score on last attempt 1 out of 3 score in gradebook 1 out of 3 a. recall that the candle burns at a constant rate of 1.8 inches per hour. complete the following statements. - $delta h=\text{______}cdotdelta t$ preview - $\frac{delta h}{delta t}=\text{______}$ preview b. 5.6 hours after being lit, the candle is 9.92 inches tall. what is the reference point $(t,h)$ given in the problem description? $(t,h)=(5.6,9.92)$ preview submit

Explanation:

Step1: Determine change in height per hour

Since the candle burns at 1.8 inches per hour, $\Delta h=- 1.8\cdot\Delta t$ (negative as height decreases).

Step2: Calculate rate of change

$\frac{\Delta h}{\Delta t}=-1.8$

Step3: Identify reference point

Given 5.6 hours and 9.92 - inch height, reference point is $(t,h)=(5.6,9.92)$

Answer:

a. $\Delta h=-1.8\cdot\Delta t$, $\frac{\Delta h}{\Delta t}=-1.8$
b. $(t,h)=(5.6,9.92)$