Final answer:
The height of the candle after 21 hours is 24.25 cm.
Step-by-step explanation:
To find the height of the candle after 21 hours, we need to determine the rate at which the height changes over time. Since the height of the candle is a linear function of the amount of time it has been burning, we can express this relationship as an equation of the form y = mx + b, where y represents the height, x represents the time, m represents the rate of change, and b represents the initial height of the candle.
Using the given information, we can form two equations:
Equation 1: 27 = 10m + b
Equation 2: 23.4 = 24m + b
By solving this system of equations, we can determine the values of m and b. Subtracting Equation 1 from Equation 2, we get:
23.4 - 27 = 24m - 10m + b - b
-3.6 = 14m
Simplifying, we find that m = -0.25.
Substituting the value of m into Equation 1, we get:
27 = 10(-0.25) + b
Solving for b, we find that b = 29.5.
Finally, we can use the equation y = mx + b to calculate the height of the candle after 21 hours:
y = (-0.25)(21) + 29.5 = 24.25 cm.