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The table below represents an exponential function.


table represents an exponential function.

What is the interval between neighboring
x-values shown in the table?

What is the ratio between neighboring y-values?

The table below represents an exponential function table represents an exponential function What is the interval between neighboring xvalues shown in the table class=

Respuesta :

[tex]\bf \begin{array}{cccccccllll} x&0&1&2&3&4&5\\ y&1&4&16&?&256&1024\\ -&-&-&-&-&-&-\\ &&1\cdot \underline{4}&4\cdot \underline{4}&16\cdot \underline{4}&?\cdot \underline{4}&256\cdot \underline{4} \end{array}[/tex]

notice, the first value is 1, but any subsequent values are just the product of 4 and the current value.  Thus the "common ratio" is 4.

In given table of exponential function,

The interval between neighboring  x-values is of 1 unit.

The ratio is  4  between neighboring y-values

Observing given table.

To find  interval between neighboring  x-values . We have to take difference between consecutive x - values.

[tex]1-0=2-1=3-2=4-3=5-4=1[/tex]

Since, in every consecutive x- values , difference of 1 is present.

So, The interval between neighboring  x-values is of 1 unit.

To find ratio between neighboring y-values , we have to take ratio of consecutive y - values.

     [tex]\frac{4}{1}=\frac{16}{4}=\frac{64}{16}=\frac{256}{64}=4[/tex]

Thus, The ratio is  4  between neighboring y-values

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