The table represents an exponential function. a 2-column table has 4 rows. the first column is labeled x with entries 1, 2, 3, 4. the second column is labeled y with entries 6, 4, eight-thirds, sixteen-ninths. what is the multiplicative rate of change of the function?

The multiplicative rate of change of the function is

Step-by-step explanation:

You are given the table

An exponential function can be written as

where b is the multiplicative rate of change of the function.

Find a and b. Substitute first two corresponding values of x and y into the function expression:

Divide the second equality by the first equality:

Substitute it into the first equality:

So, the function expression is

Check whether remaining two values of x and y suit this expression:

So, the multiplicative rate of change of the function is

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

207/8 is the right