1.
What do you know?
the troposphere extends 8 to 20 km above the Earth's surface. The surface temperature is 15°C and decreases at a rate of 6.5°C per kilometer away.
What do you want to find out?
The temperature at any point of the troposphere
What kind of answer do you expect?
Any value below 15°C
2. Define variables,
T is for temperature, and
d is the distance away from the surface
3. What is the b -value
b = 15
which is the Earth's surface temperature or the initial temperature for our problem
4. What is the slope
the slope 'm' equals -6.5
which means that the temperature decreases 6.5°C per km
5. write the equation
[tex]\begin{gathered} y=b+mx \\ \Rightarrow T=15-6.5d \end{gathered}[/tex]
the general form for this equations is y = b + mx
thus, for our problem, the equation is: T = 15 - 6.5*d
6.
a) the slope represents the rate of change of temperature with respect to distance, since m = -6.5 °C/km , this means the troposphere is getting 6.5 °C colder per km away from Earth's surface
b) the y-intercept represents the Earth's surface temperature
Graph:
7. identify 3 points
when d = 0 then T = 15, so our first point is (0,15)
when d = 1 then T = 15 - 6.5 = 8.5 , so our second point is (1,8.5)
when d = 2 then T = 15 - 13 = 2 so our third point is (2,2)
8. calculate the slope
let's use this equation and this set of points,
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ (x1,y1)=(1,8.5) \\ (x2,y2)=(2,2) \end{gathered}[/tex]
let's replace and solve
[tex]m=\frac{2-8.5}{2-1}=\frac{-6.5}{1}=-6.5[/tex]
We can see that it does match the slope from our model, which is -6.5
9. graph the line and the points,
10. Complete the sentence
... ends between 8 km and 20 km above Earth.
11. temperature at the farthest point
when d = 20 then,
[tex]\begin{gathered} T=15-6.5*20 \\ =15-130 \\ =-115 \end{gathered}[/tex]
... the temperature is -115°C
12. Temperature range,
from... 15 °C to -115 °C
