Chapter 8.6, Problem 67PPS

a.

To determine

To create the table of values for the given function using graphing calculator and then find $x$ when $y=13$

Answer to Problem 67PPS

  $x=1.85$

Explanation of Solution

Given:

The given equation is $y=4^x$

Calculation:

Consider the given equation $y=4^x$ .

After graphing the table using the Graph option of the graphing calculator, following snapshot is obtained

  

Therefore

  $\begin{array}{l}{4}^{1.85}=12.996\\ \approx 13\end{array}$

Therefore, the required value $x=1.85$

b.

To determine

To create point of intersection using the intersect feature.

Answer to Problem 67PPS

  $x=1.85$

Explanation of Solution

Given:

The given equation is $y=4^x$

Calculation:

Consider the given equation $y=4^x$ and $y=13$

After graphing the table using the Graph option of the graphing calculator, following snapshot is obtained

  

Therefore the intersection of two curves is

  $\begin{array}{l}x=1.8502199\\ y=13\end{array}$

Therefore, the required value $x=1.85$

c.

To determine

To solve the equation algebraically and compare the results.

Answer to Problem 67PPS

  $x=1.8502$

Explanation of Solution

Given:

The given equation is $4^x=13$

Calculation:

Consider the given equation.

  $\begin{array}{l}{4}^x=13\\ \log 4^x=\log 13\\ x\log 4=\log 13\\ x=\frac{\log 13}{\log 4}\\ x=1.8502\end{array}$

So, all the methods will produce the same results, only difference is in the accuracy of the result.