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 17 centimeters. After 21 hours of burning, its height is 12.6 centimeters. What is the height of the candle after 14 hours?

The height of the candle after 14 hours is 15.4 centimeters

Step-by-step explanation:

A linear function is a polynomial function of the first degree of the form:

f(x)= m*x + b or y= m*x + b

where m is the slope of the function and b is the ordinate at the the y-intercept.

In this case height=m*time + b

Given two points of the line, point 1 (x1, y1) and point 2 (x2, y2), we can find the equation of the line or linear function.

You must first find the slope of the line using the expression:

In this case you know the two points are (x1, y1)= (10,17) and (x2, y2)=(21,12.6)

So the slope is:

m= -0.4

Now you find the value of b, replacing m in the equation, the values of x and y by the values of the coordinates of one of the points and solving for b to obtain its value.

Replacing (x1, y1)= (10,17) and m=-0.4 in the expresion y=m*x+b:

17= -0.4*10 + b

and solving you get:

17= -4 + b

17 + 4= b

21= b

So: height= -0.4*time + 21 where the height is expressed in centimeters and the time in hours.

To calculate the height of the candle after 14 hours, you simply replace the time by 14:

height= -0.4*14 + 21

height= 15.4

The height of the candle after 14 hours is 15.4 centimeters

an altitude of 15,000 feet

step-by-step explanation: