identify the type of variation represented in the table and name the y-value when x=32. x: 2,4,8,16, 32 y: 4, 2, 1, 0.5, ?

Well, the type of variation shown in the table is called "inverse variation" or "inverse proportion." As for the y-value when x=32, let's see if we can figure it out using some mathematical humor.

When x doubles from 16 to 32, the y-values also double. So, if we follow this pattern, we can assume that when x=32, the y-value will be 0.25.

Why 0.25? Well, clowns love to juggle numbers, and in this case, we're juggling fractions. Just imagine our clown friend tossing around the decimal point, landing it perfectly in front of that 2. So, when x=32, the y-value is 0.25!

To identify the type of variation represented in the table, we need to observe the relationship between the x-values and the corresponding y-values.

First, let's examine the ratio between consecutive y-values:

- The ratio between 4 and 2 is 4/2 = 2.
- The ratio between 2 and 1 is 2/1 = 2.
- The ratio between 1 and 0.5 is 1/0.5 = 2.

We can see that the ratio between consecutive y-values is constant, which means that the variation represented in the table is an inverse variation.

To find the y-value when x = 32, we can use the inverse variation equation:

\[ xy = k \]

where k is the constant of variation.

Using the given values (x,y) = (2,4), we can calculate the value of k:

\[ (2)(4) = k \Rightarrow k = 8 \]

Now, we can use this value of k to find the y-value when x = 32:

\[ (32)(y) = 8 \Rightarrow y = \frac{8}{32} = 0.25 \]

Therefore, when x = 32, the y-value is 0.25.

To identify the type of variation represented in the table, we need to observe the relationship between the values of x and y. In this table, as x doubles, y is halved.

This type of variation is called inverse variation, also known as inverse proportion or inversely proportional relationship. In inverse variation, as one variable increases, the other variable decreases in inverse proportion.

To find the y-value when x = 32, we can use the inverse variation relationship observed in the table. As x doubles, y is halved. Starting with an x-value of 2, we can see that when x doubles successively (2, 4, 8, 16, 32), y is halved each time (4, 2, 1, 0.5, ?).

Therefore, when x = 32, y would be half of the previous value, which is 0.5. Therefore, the y-value when x = 32 is 0.5.

every x value is twice the previous

every y value is half the previous
so if x = 32 then y = 0.25

well if n = 1 is your first point and n = 2 is your second etc then
x = 2^n
and
y = 4/2^(n-1) = 2^2 * 2^(1-n) =2^(3-n)
so
x/y = 2^n/2^(3-n) = 2^(2n-3)
y = x * 2^(3-2n)