Question

The table below represents the atmospheric temperature at a location as a function of the altitude:

Altitude
(in thousand feet)
x
15
20
25
30

Temperature
(in °C)
f (x)

4
−6
−16
−26


The average rate of change of the function between x = 15 to x = 25 is ___degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.

Answer 1

Answer: The average rate of change of the function between x = 15 to x = 25 is -2 degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.

Explanation:

The average rate of change of a function y=f(x) from
`x_1\ to\ x_2`is given by :-

`k=(f(x_2)-f(x_1))/(x_2-x_1)=(-6-4)/(20-15)`

Now, by the given table the average rate of change of the function between x = 15 to x = 25 will be :_

`k=(-16-4)/(25-15)=(-20)/(10)=-2`

Hence, the average rate of change of the function between x = 15 to x = 25 is -2 degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.

Answer 2

from x15 to x 25 is 4 - -16 = -20 degree change

25 -15 = 10000 feet

-20/10 = -2 degrees every 1000 feet