In the troposphere, as altitude increases, air temperature drops at a relatively uniform rate. At the top of the troposphere, an average depth of 11 km, the average temperature is -56.5°C. At the base of the troposphere, 0 km, the average temperature is 15°C.

In a linear model of this situation, which of the following statements applies?
An increase of 1 km in altitude corresponds to a increase of 6.5°C in temperature.

An increase of 1 km in altitude corresponds to a decrease of 3.8°C in temperature.

An increase of 1 km in altitude corresponds to a increase of 3.8°C in temperature.

Question

In the troposphere, as altitude increases, air temperature drops at a relatively uniform rate. At the top of the troposphere, an average depth of 11 km, the average temperature is -56.5°C. At the base of the troposphere, 0 km, the average temperature is 15°C. 

In a linear model of this situation, which of the following statements applies?
An increase of 1 km in altitude corresponds to a increase of 6.5°C in temperature.

An increase of 1 km in altitude corresponds to a decrease of 3.8°C in temperature.

An increase of 1 km in altitude corresponds to a increase of 3.8°C in temperature.

jademc01 · Answer

In a linear model of this situation, the y-intercept represents the temperature at the base of the troposphere, 15°C.

The rate of change, or slope, can be determined using two values: temperature at base, (0, 15), and temperature at top, (11, -56.5).



The linear model of this situation is y = 15 - 6.5x, where x represents the depth of the troposphere, in kilometers.

The rate of change, or slope, indicates that an increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature.