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Look for a pattern in each table of values to determine which kind of model best describes the data. Then write an equation for the function that models the data.

x

0

1

2

3

4

y

1

2

4

8

16

Short Answer

Expert verified

The equation of the function that models best the given data is y=2x.

Step by step solution

01

Step 1. Determine the first difference, second differences or ratio of successive values.

Find the first differences, second differences or ratio of successive values as required.

First difference:

Second difference:

Ratio of successive values:

02

 Step 2. Write an equation for the functions that models the data. 

Since the ratios of successive y–values are equal; the table of values represents an exponential function of the form y=abx. The constant ratio is 2, so b=2.

03

Step 3. Simplify the equation for the function.

To find a, use an ordered pair from the table, such as (0,1).

y=abx1=a×20        [  x=0,y=1  ]1=ay=1×20=2x

Therefore, the equation that models the data is y=2x.

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