Chapter 7.6, Problem 1P

Determine whether each table or rule represents a linear or an exponential function. Explain.

To determine

Whether the given table represents a linear of exponential function.

Answer to Problem 1P

The table represents an exponential function $y=3^x$ .

Explanation of Solution

Given information:

The table for function $y=f\left(x\right)$ is given below:

  

Method used:

From the given data a relationship between x and y is observed.

Calculations:

From the given table, the relationship between values of x and y is

  $3=3^1$ , $9=3^2$ , $27=3^3$ , and $81=3^4$ .

Thus, in terms of x and y the relationship is $y=3^x$ that an exponential relation.

Hence, the table represents an exponential function.

Conclusion:

The table represents an exponential function $y=3^x$ .