Question

Helpp please

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 14 hours of burning, a candle
has a height of 21.2 centimeters. After 32 hours of burning, its height is 17.6 centimeters. What is the height of the candle after 26 hours?

Answer 1

Explanation:

We are given two points on a line: (14, 21.2) and (32, 17.6). Let h be the height of the candle after t hours. We want to find h when t = 26.

Since the height is a linear function of time, we can write the equation of the line in point-slope form:

h - 21.2 = m(t - 14)

where m is the slope of the line. To find the slope, we use the two points:

m = (17.6 - 21.2)/(32 - 14) = -0.18

Substituting m = -0.18 and one of the points (14, 21.2) into the equation, we get:

h - 21.2 = -0.18(t - 14)

h - 21.2 = -0.18t + 2.52

h = -0.18t + 23.72

To find the height of the candle after 26 hours, we substitute t = 26:

h = -0.18(26) + 23.72

h = 19.48

Therefore, the height of the candle after 26 hours is 19.48 centimeters.