Does the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table. X:2,4,8,12 Y:6,3,3/2,1

- Inverse Variation

- Equation:

Step-by-step explanation:

Given

X-> 2 | 4 | 8 | 12

Y-> 6 | 3 | 3/2 | 1

Required

- State the type of variation the table represents

- Determine the equation to model the data

To check for type of variation; we'll make use of trial by error method.

To start with; We'll check for direct variation.

This is done using the following expression;

where k is the constant of variation

Make k the subject of formula

When Y = 6, X= 2

When Y = 3, X = 4

There's no need to check further as both values of k are not equal

To check for inverse variation;

Make k the subject of formula

When Y = 6, X= 2

When Y = 3, X = 4

When Y = 3/2; X = 8

When Y = 1, X = 12

Note that for all values of X and Y, K remains constant;

Hence, the table represents an inverse direction

To determine the equation;

We make use of  

Substitute 12 for k

So, the equation becomes

Reorder

Hence, the equation is

the nearest power is 1.651.

means 7482 to the 1.651th power is almost equal to 2489287