the height (in cm) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with s slope of -0.4
suppose the height of the candle after 14 hours is 18.45 centimeters. What will be the height of the candle after 22 hours.
To find the height of the candle after 22 hours, we need to use the information given about the linear function and the height after 14 hours.
Given that the height of the candle is a linear function of time with a slope of -0.4, we can represent the function as:
h(time) = -0.4 * time + b
where h(time) is the height of the candle at a given time, and b is the y-intercept.
We also know that after 14 hours, the height is 18.45 centimeters. We can substitute these values into the equation to find the y-intercept, b.
18.45 = -0.4 * 14 + b
Now, let's solve for b:
18.45 = -5.6 + b
b = 18.45 + 5.6
b = 24.05
So, the equation of the linear function representing the height of the candle is:
h(time) = -0.4 * time + 24.05
Now, we can plug in 22 for time to find the height of the candle after 22 hours:
h(22) = -0.4 * 22 + 24.05
h(22) = -8.8 + 24.05
h(22) = 15.25
Therefore, the height of the candle after 22 hours will be 15.25 centimeters.