The table represents an exponential function. What is the multiplicative rate of change of the
function?
Х
1
3
.
2.
4
9
16
9

Step-by-step explanation:

An exponential function has a standard form

where a is the initial value, b is the rate of growth or decay, and x and y are found in coordinates from the table. We need to solve for b, the rate of change (growth or decay). We will use the first 2 coordinates in the table, namely (1, 6) and (2, 4) to solve for b. We will use a system of equations...2 equations for 2 unknowns. The first equation is found by plugging in a 6 for y and a 1 for x to get:

and, solved for a:

.

In the second equation, we will plug in a 4 for y, a 2 for x and the value for a we just found:

and, simplified a bit:

which finally simplifies to

4 = 6b and

. That's the rate of change we are asked to find. We could continue to find the whole equation. Plug in 2/3 for b to solve for a:

and

and the exponential equation is

that means that we started with 9 of something and it is dying/decaying/depreciating at a rate of 33%

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.