SAT Mathematics Practice Test 4

Question : 20 of 58

Marks: +1, -0

The mesosphere is the layer of Earth’s atmosphere between 50 kilometers and 85 kilometers above Earth’s surface. At a distance of 50 kilometers from Earth’s surface, the temperature in the mesosphere is

−5°

Celsius, and at a distance of 80 kilometers from Earth’s surface, the temperature in the mesosphere is

−80°

Celsius. For every additional 10 kilometersfrom Earth’s surface, the temperature in the mesosphere decreases by

k °

Celsius, where k is a constant. What is the value of

k

Your Answer:

Validate

Solution:

In the mesosphere, an increase of 10 kilometers in the distance above Earth results in a decrease in the temperature by

k °

Celsius where k is a constant. Thus, the temperature in the mesosphere is linearly dependent on the distance above Earth. Using the values providedand the slope formula, one can calculate the unit rate of change for the temperature in the mesosphere to be

{-80-(-5)}/{80-50}={-75/30={-2.5/1}}

The slope indicates that, within the mesosphere, if the distance above Earth increases by 1 kilometer, the temperature decreases by

2.5°

Celsius. Therefore, if the distance above Earth increases by

(1×10)=10

kilometers, the temperature will decrease by

(2.5×10)=25°

Celsius. Thus, the value of k is

25

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