A 16-inch candle is lit and burns at a constant rate. After 30 minutes, the candle is 12 inches tall. Which linear equation models the relationship between h, the height of the candle in inches, and t, the time in hours that it has burned?
h = 16 - (16-12)/0.5h
h = 16 - 8in/h
Eq: h(t) = 16 - 8t
To find the linear equation that models the relationship between the height of the candle (h) and the time it has burned (t), we need to start by converting the given information into a consistent unit of measurement.
We are given that the candle burns at a constant rate and after 30 minutes, it is 12 inches tall. We want to express the time in terms of hours, so we convert 30 minutes to hours by dividing it by 60 (since there are 60 minutes in an hour).
30 minutes ÷ 60 = 0.5 hours
So, after 0.5 hours, the candle height is 12 inches.
Next, we can set up the linear equation using the slope-intercept form:
y = mx + b
where y is the dependent variable (height), m is the slope (rate of burning), x is the independent variable (time), and b is the y-intercept (initial height).
Since the height decreases as time passes, the slope will be negative. Additionally, we know that when t = 0 (at the beginning), the height is 16 inches. Therefore, the equation becomes:
h = mt + b
Given that after 0.5 hours, the height is 12 inches, we have the following values:
h = 12
t = 0.5
b = 16 (initial height)
Substituting these values into the equation, we can solve for the slope (m):
12 = m(0.5) + 16
Rearranging the equation:
12 - 16 = 0.5m
-4 = 0.5m
To isolate m, divide both sides by 0.5:
m = -4 ÷ 0.5
m = -8
Therefore, the linear equation that models the relationship between the height (h) and the time (t) is:
h = -8t + 16