Chapter 7.5, Problem 47PFA

To determine

To find which equation and y- intercept suits the given graph.

Answer to Problem 47PFA

  $y=4^x$

Explanation of Solution

Given:

  

Concept used:

Find the point from the graph, which meets the y axis. Substitute in the equation to find the solution.

Calculation:

From the graph, we could see that the curve meets the y axis at $\left(0,1\right).$

Therefore, substitute $x=0$ in the equation find the value of y if it is 1, the given graph is the graph of the function.

Now, Substitute the points in each of the equations, same solution is for the following equations.

  $y=4^x$

  $\begin{array}{l}\Rightarrow y=4^0\\ \Rightarrow y=1\end{array}$

And $y={\left(\frac{1}{4}\right)}^x$

  $\begin{array}{l}\Rightarrow y={\left(\frac{1}{4}\right)}^0\\ \Rightarrow y=1\end{array}$

For $y={\left(\frac{1}{4}\right)}^x$ , the curve moves to the infinity towards the right of the origin.

In the given graph, the curve moves towards infinity towards the left of origin.

Therefore, the equation that best suits the given graph is $y=4^x.$

Conclusion:

Therefore, the equation of the given graph is $y=4^x.$