The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line With slope of —0.4. See the figure below. Suppose that the height of the candle after 11 hours is 22.6 centimeters. What was the height of the candle after 2 hours?
the slope means that the candle shortens by .4 cm per hour of burning
how much taller would it be nine hours earlier? (how much did it shrink in nine hours?)
To find the height of the candle after 2 hours, we can use the information given:
1. The function representing the height of the candle is linear, which means it can be written in the form: height = slope * time + intercept.
2. The slope of the function is given as -0.4. This means that for every hour the candle is burning, its height decreases by 0.4 centimeters.
3. We need to find the height of the candle after 2 hours. Let's denote the height after 2 hours as h2.
Using the slope-intercept form, we have:
h2 = -0.4 * 2 + intercept.
To determine the intercept, we can use the information given in the problem. We know that after 11 hours, the height of the candle is 22.6 centimeters. Let's denote this as h11.
Using the slope-intercept form again, we have:
h11 = -0.4 * 11 + intercept.
Now, we can solve for the intercept by rearranging the equation:
intercept = h11 + 0.4 * 11.
Substituting this value back into the equation for h2:
h2 = -0.4 * 2 + (h11 + 0.4 * 11).
Then, simplify the equation:
h2 = -0.8 + h11 + 4.4.
Combine like terms:
h2 = h11 + 3.6.
Finally, substitute the given value of h11 (22.6) into the equation:
h2 = 22.6 + 3.6.
Evaluate the expression:
h2 = 26.2.
Therefore, the height of the candle after 2 hours is 26.2 centimeters.