Chapter 7, Problem 8PFA

To determine

The equation of the function which represents the table of data given.

Answer to Problem 8PFA

The equation of the function is $y=6{(2)}^x$ .

Explanation of Solution

Given information: A table of data given, with points $(0,6)$ , $(1,12)$ , $(2,24)$ and $(3,48)$ .

Calculation:

Let, the equation of the function be $y=a{b}^x$ .

By taking the point $(0,6)$ and plugging in $x=0$ and $y=6$ ,

  $\begin{array}{l}y=a{b}^x\\ \Rightarrow 6=a{b}^0\\ \Rightarrow 6=a(1)\\ \Rightarrow 6=a\\ \therefore a=6\end{array}$

The equation of the function becomes $y=6b^x$ .

Now by taking the point $(1,12)$ and plugging in $x=1$ and $y=12$ ,

  $\begin{array}{l}y=6b^x\\ \Rightarrow 12=6b^1\\ \Rightarrow 6b=12\\ \Rightarrow b=\frac{12}{6}\\ \Rightarrow b=2\end{array}$

So, the equation of the function is $y=6{(2)}^x$ .

Option A is correct.