Question

h(t) = ⅝t - 9| t | q(t) || 0 | -9 || 1 | -8.25 || 2 | -7.5 || 3 | -6.75 |Which function increases faster?A) hB) qC) The functions increase at the same rate.

Answer 1

Notice that we are actually given the rate at which function h(t) is increasing, since it is shown in the SLOPE of the line:

h(t) = 5/8 t -9

The rate is 5/8 for this function.

So we need to find the rate for the function given by the table, and we do such by finding the slope of the line or segment that joins any two points of that table. For example, we use the points: (0, -9) and (2, - 7.5)

in the equation for the slope:

slope = (y2 - y1) / (x2 - x1)

in our case:

slope of q(t) = (-7.5 - - 9) / (2 - 0) = 1.5 / 2 = 0.75 = 3/4

we know that 3/4 is the same as 6/8

so when we compare the rates:

rate of h(t) = 5/8

rate of q(t) = 6/8

we conclude that function q(t) increases at a faster rate

So, please select answer B