Question

n certain​ conditions, the air temperature drops about 3.6F for each​ 1,000-foot rise in altitude.
​(A) If the temperature at sea level is 65​F, write a linear equation that expresses the temperature T in terms of altitude A in thousands of feet.
​(B) At what altitude is the temperature 11
​F?

Answer 1

(A) To write a linear equation that expresses the temperature T in terms of altitude A in thousands of feet, we can use the given condition that the temperature drops about 3.6F for each 1,000-foot rise in altitude.

Let's assume that at sea level (A = 0), the temperature is T = 65F. As the altitude increases by 1,000 feet (A = 1), the temperature drops by 3.6F.

Therefore, the equation that expresses the temperature in terms of altitude is:

T = 65 - 3.6A

(B) To find the altitude at which the temperature is 11F, we can substitute T = 11 into the equation we obtained in part (A) and solve for A.

11 = 65 - 3.6A

Rearranging the equation, we get:

3.6A = 65 - 11

3.6A = 54

Dividing both sides by 3.6, we have:

A = 54/3.6

A = 15

Therefore, the altitude at which the temperature is 11F is 15,000 feet.