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%

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form