The stopping distance at some fixed speed of regular tires o

The stopping distance (at some fixed speed) of regular tires on glare ice is a function of the air temperature F, in degrees Fahrenheit. This function is estimated by D(F) = 2F+115, where D(F) is the stopping distance, in feet, when the air temperature is F, in degrees Fahrenheit. (a) Find D(0degrees), D(-20degrees), D(32degrees). (b) Explain why the domain should be restricted to [-57.5degrees,32degrees].

Solution

Given :

D(F) = 2F + 115

#(a)

For, D(0) plug F = 0 into D(F) , we get:

D(0) = 2(0) + 115

Hence, D(0) = 0+115

D(0) = 115

For D(-20) , plug F = -20 into D(F) , we get:

D(-20) = 2(-20) + 115

= -40 + 115

= 75

Hence, D(-20) = 75

Now for D(32) plug F = 32 into D(F) , we get:

D(32) = 2(32) + 115

= 64 + 115

= 179

Hence, D(32) = 179

#(b)

The Domain should be restricted to [-57.5, 32] for two reasons. First, it should be 32 because ice will melt at any temperature above 32 degrees Fahrenheit. Second, it should be -57.5 because at that temperature, D(-57.5)=0, anything lower and you will get negative stopping distances which are impossible.