Chapter 8.6, Problem 24E

To determine

To describe:the nature of the function.

Answer to Problem 24E

The function that describes the given data is $f\left(x\right)={5.2}^x$

Explanation of Solution

Given information:

A table of data is given

  

Calculation:

The given data does not have constant first or second difference. The next y value determines on multiplying a common ration of 2. Thus the data describes the exponential function with a base 2.

Equation of a function with base 2 would be

  $f\left(x\right)=a{.2}^x$

Use any point such as $\left(0,5\right)$ In order to get the value of ‘a’

  $\begin{array}{l}5=a{.2}^0\\ 5=a\left(1\right)\\ 5=a\end{array}$

Substituting the value of a into the original equation

  $f\left(x\right)={5.2}^x$

Thus the function that represents the given table of data is $f\left(x\right)={5.2}^x$

Conclusion:

The function that describes the given data is $f\left(x\right)={5.2}^x$