Chapter 9, Problem 60SGR

To determine

Find the equation that describes best the data.

Answer to Problem 60SGR

The equation models best the given data is $y=2^x$

Explanation of Solution

Given:

  

Concept Used:

First difference:

  

Second difference:

  

Ratio of successive values:

  

Since the ratios of successive y − values are equal; the table of values represents an exponential function of the form $y=a{b}^x$ . The constant ratio is 2, so $b=2$ ,

Calculation:

Since the ratios of successive y − values are equal; the table of values represents an exponential function of the form $y=a{b}^x$ . The constant ratio is 2, so $b=2$ ,

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

  $\begin{array}{l}y=a{b}^x\\ 1=a·2^0[x=0,y=1]\\ 1=a\\ y=1·2^0=2^x\\ y=2^x\end{array}$ An equation that models the data is $y=2^x$

Thus, an equation that models the data is $y=2^x$