Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 11 hours of burning, a candle has a height of 16.4 centimeters. After 26 hours of burning, its height is 7.4 centimeters. What is the height of the candle after 18 hours?BurningtimeinhoursCandleheightincm

To solve this problem, we first need to find the rate at which the candle is burning. We know that the height of the candle decreases over time, so this rate will be negative.

Step 1: Find the rate of change (slope) The rate of change is equal to the change in height divided by the change in time. We can calculate it as follows:

Rate of change = (Height2 - Height1) / (Time2 - Time1) Rate of change = (7.4 cm - 16.4 cm) / (26 hours - 11 hours) Rate of change = -9 cm / 15 hours Rate of change = -0.6 cm/hour

This means that the candle burns at a rate of 0.6 cm per hour.

Step 2: Find the initial height (y-intercept) We can use the point-slope form of a linear equation to find the initial height of the candle. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is a point on the line. We can use the point (11 hours, 16.4 cm) and the slope we found in step 1:

16.4 cm - y = -0.6 cm/hour * (11 hours - x) y = 16.4 cm + 0.6 cm/hour * (11 hours - x)

Step 3: Find the height after 18 hours Substitute x = 18 hours into the equation we found in step 2:

y = 16.4 cm + 0.6 cm/hour * (11 hours - 18 hours) y = 16.4 cm - 0.6 cm/hour * 7 hours y = 16.4 cm - 4.2 cm y = 12.2 cm

So, the height of the candle after 18 hours is 12.2 cm.