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.
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.
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.