The table below lists braking distance (in meters) vs starting speed (in kilometers per hour). What is the nature of the relationship of the values? If the length of some skid marks is #104# meters, then what was the driver's estimated initial speed?

Make a plot of the points first:

graph{((x-0)^2+(y-0)^2-1.5)((x-10)^2+(y-0.7)^2-1.5)((x-20)^2+(y-2.8)^2-1.5)((x-30)^2+(y-6.3)^2-1.5)((x-40)^2+(y-11.2)^2-1.5)((x-50)^2+(y-17.5)^2-1.5)((x-60)^2+(y-25.2)^2-1.5)((x-70)^2+(y-34.3)^2-1.5)((x-90)^2+(y-56.7)^2-1.5)((x-100)^2+(y-70)^2-1.5) = 0 [-160, 160, -80, 80]}

That appears to be a curve as opposed to a straight line.

As the table illustrates, the skid distance actually quadruples when the speed doubles.

A pure quadratic relationship exists there.

Fitting the function is possible:

graph{((x-0)^2+(y-0)^2-1.5)((x-10)^2+(y-0.7)^2-1.5)((x-20)^2+(y-2.8)^2-1.5)((x-30)^2+(y-6.3)^2-1.5)((x-40)^2+(y-11.2)^2-1.5)((x-50)^2+(y-17.5)^2-1.5)((x-60)^2+(y-25.2)^2-1.5)((x-70)^2+(y-34.3)^2-1.5)((x-90)^2+(y-56.7)^2-1.5)((x-100)^2+(y-70)^2-1.5)(y-0.007x^2) = 0 [-160, 160, -80, 80]}

So:

and

To determine the nature of the relationship between the braking distance and the starting speed, we can plot the data and analyze the trend. Once we identify the nature of the relationship, we can estimate the initial speed given a braking distance.

Without the table of values, it's not possible to determine the exact nature of the relationship or estimate the initial speed given a braking distance. If you provide the table of values, I can assist you further in analyzing the data and answering the question.