Question

The freezing point of water, T (measured in degrees Fahrenheit), at altitude a (measured in feet) is modeled by the function T(a) = .0001a +32. In terms

of altitude and temperature, which statement describes the meaning of the slope?

Answer 1

The freezing point of water increases by 0.0001 degrees Fahrenheit when the altitude increases by 1 foot.

Explanation:

The model for the freezing point of water T at altitude a is:

T(a)= 0.0001a+32

The slope of this equation is the coefficient of the variable a. Since the slope is positive, it means the freezing point of water increases by 0.0001 degrees Fahrenheit when the altitude increases by 1 foot.

For example, when a=1000, the freezing point is:

T(1000)= 0.0001*1000+32 = 32.1°F

When a=1001, the freezing point is:

T(1001)= 0.0001*1001+32 = 32.1001°F

Note the increase of 1 foot in altitued meant an increase of 32.1001-32.1 = 0.0001°F