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 11 hours of burning, a candle has a height of 18.6 centimeters. After 27 hours of burning, its height is 12.2 centimeters. What is the height of the candle after 15 hours?

Calculate how much height it loses per hour. Call it m.

m = (18.6 - 12.2)/16 = ___ cm/h

Then solve
(candle height) y = 12.2
= 18.6 - m(t - 11)
using t = 15

It's called interpolation.

thanks for the help

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 10 hours of burning, a candle has a height of 24 centimeters. After 27 hours of burning, its height is 20.6 centimeters. What is the height of the candle after 21 hours?

i don't know the answer at all tall my now

To find the height of the candle after 15 hours, we need to determine the equation of the linear function that describes the relationship between the height of the candle and the amount of time it has been burning.

Let's assume that the height of the candle, h, is a linear function of the time, t. The general form of a linear function is given by:

h = mt + b

Where m is the slope (rate of change) of the function and b is the y-intercept (the value of h when t is 0).

To find the values of m and b, we can use the given information. We have two data points: (11, 18.6) and (27, 12.2). Plugging these values into the equation, we can set up two equations to solve for m and b.

First, using the data point (11, 18.6):

18.6 = 11m + b

And using the data point (27, 12.2):

12.2 = 27m + b

Now, we have a system of two equations with two variables (m and b). We can solve this system of equations to find the values of m and b.

Subtracting the second equation from the first equation, we get:

(18.6 - 12.2) = (11m + b) - (27m + b)
6.4 = 11m - 27m

Combining like terms, we have:

6.4 = -16m

Dividing both sides by -16, we get:

m = -0.4

Now, we can substitute this value of m into either of the original equations to solve for b. Let's use the equation (11, 18.6):

18.6 = 11(-0.4) + b
18.6 = -4.4 + b

Adding 4.4 to both sides, we get:

23 = b

So, we have found the values of m and b. The equation that describes the relationship between the height of the candle (h) and the time (t) is:

h = -0.4t + 23

To find the height of the candle after 15 hours, we can plug t = 15 into the equation:

h = -0.4(15) + 23
h = -6 + 23
h = 17

Therefore, the height of the candle after 15 hours of burning is 17 centimeters.