Chapter 6.4, Problem 12Q

To determine

Whether the table represents an exponential growth function, an exponential decay function, or neither.

Answer to Problem 12Q

The function that represents the table would be $f(x)=7{(3)}^x$ with $a>0,b>1$ . Therefore, the table represents the exponential growth function.

Explanation of Solution

Giveninformation:

The table is

$x$	0	1	2	3
$f(x)$	7	21	63	189

From the table values, we can notice the following results:

  $\begin{array}{l}7=7\cdot 3^0\\ 21=7\cdot 3=7\cdot 3^1\\ 63=7\cdot 9=7\cdot 3^2\\ 189=7\cdot 27=7\cdot 3^3\end{array}$

So the function that represents the table would be $f(x)=7{(3)}^x$ .

Conclusion:

Now, comparing the function with $f(x)=a{b}^x$ , we can observe that $a>0,b>1$ . Therefore, the table represents the exponential growth function.