Question

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 12 hours of burning, a candle
has a height of 25.2 centimeters. After 25 hours of burning, its height is 20 centimeters. What is the height of the candle after 17 hours?

Answer 1

Answer:

25 cm

Step-by-step explanation:

We need to derive a linear function satisfied by the given points (12 hrs, 25.2 cm) and (25 hrs, 20 cm)

Going from point (12 hrs, 25.2 cm) to (25 hrs, 20 cm), time t increases by 13 hrs and height h decreases by 5.2 cm.  Thus, the slope of this linear function is

m = rise/run = -5.2 cm  /  13 hrs = -0.4 cm/hr

Using the point (12 hrs, 25.2 cm) and the slope -0.4 cm/hr in the point-slope formula of the equation of a straight line, we get:

y - 25.2 cm = (-0.4 cm/hr)(x - 12 hr).

where y is the height of the candle after x hours.

After 17 hours, y - 25.2 cm = (-0.4 cm/hr)(x hr - 12 hr) becomes

                        y - 25.2 cm = (-0.4 cm/hr)(17 hr - 12 hr), so that

                         y = 25.2 cm -0.4(5) cm = 25.2 cm - 0.2 cm) ] 25 cm