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Nadya [2.5K]
3 years ago
6

Determine if the table shows a linear or an exponential function​

Mathematics
2 answers:
VMariaS [17]3 years ago
5 0
Like ya cuttt g..........
____ [38]3 years ago
4 0

Answer:

<em>The table shows an exponential function</em>

Step-by-step explanation:

<u>Linear vs Exponential Functions</u>

A linear function is written as:

y=mx+b

where m and b are constants.

If a table contains a linear function, then for each pair of ordered pairs (x1,y1) and (x2,y2), the value of m must be constant.

The slope can be calculated as:

\displaystyle m=\frac{y_2-y_1}{x_2-x_1}

An exponential function is written as:

y=y_o.r^x

Where r is the ratio and yo is a constant.

If a table contains an exponential function, for two ordered pairs (x1,y1) and (x2,y2), the value of r must be constant.

The ratio can be calculated as:

\displaystyle r=\sqrt[x2-x1]{\frac{y2}{y1}}

Calculate the slope for (0,4) and (1,2):

\displaystyle m=\frac{2-4}{1-0}=-2

Calculate the slope for (1,2) and (2,1):

\displaystyle m=\frac{1-2}{2-1}=-1

Since the slope is not the same, the function is not linear.

Now calculate the ratio for (0,4) and (1,2)

\displaystyle r=\sqrt[1-0]{\frac{1}{2}}

The radical of index 1 is simply equal to its argument:

\displaystyle r=\frac{1}{2}

Now calculate the ratio for (0,4) and (2,1)

\displaystyle r=\sqrt[2-0]{\frac{1}{4}}

\displaystyle r=\sqrt{\frac{1}{4}}

\displaystyle r=\frac{1}{2}

Testing other points we'll find the same ratio, thus the table is an exponential function

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skad [1K]

Answer:

Because this spread will add up to zero

Step-by-step explanation:

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For the values which are below the center (i.e. less than the mean), when mean is subtracted from these values, this results in negative numbers.

For the values which are above the center(i.e. greater than the mean), when mean is subtracted from these values, this results in positive numbers.

When these negative and positive numbers are summed together, as it is, they cancel out each other, leaving an answer equal to zero, which would be meaningless. As a spread of 0 would mean all data values are the same, when infact they aren't.

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