21. A candle is 17 in. tall after burning for 3 hours. After 5 hours, it is 15 in. tall. Write a linear equation to model the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8 hours. (2 points)
in 2 hours it burned 2 inches.
It must have started at 20" tall.
h(t) = 20-t
h(8) = 12
Please show your work on how you got the answer please and thank you :)
To write a linear equation that models the relationship between the height h of the candle and the time t, we need to find the slope and y-intercept of the equation.
We know that the height of the candle decreases over time, so the slope of the linear equation will be negative.
First, let's find the slope of the equation. The formula for slope is:
slope = (change in vertical distance) / (change in horizontal distance)
In this case, the change in vertical distance is the change in height of the candle, and the change in horizontal distance is the change in time.
The change in height after 3 hours is 17 in - 15 in = 2 in.
The change in time is 3 hours - 0 hours = 3 hours.
So, the slope is (2 in) / (3 hours) = 2/3.
Next, let's find the y-intercept of the equation. The y-intercept is the value of h when t = 0 (at the beginning).
From the given information, we know that the height of the candle is 17 in when time is 0 hours (at the start). So, the y-intercept is 17.
Therefore, the linear equation that models the relationship between the height h of the candle and time t is:
h = -(2/3)t + 17
To predict how tall the candle will be after burning 8 hours, we substitute t = 8 into the equation:
h = -(2/3)(8) + 17
h = -16/3 + 17
h = 17 - 16/3
h = (51 - 16)/3
h = 35/3
h ≈ 11.67
Therefore, the candle will be approximately 11.67 inches tall after burning for 8 hours.