Q. 15 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 15–24, approximate each number using a calculator. Express your answer rounded to three decimal places.

(a) $3^{2.2}$

(b) $3^{2.23}$

(c) $3^{2.236}$

(d) $3^{\sqrt{5}}$

Step-by-Step Solution

Answer

The approximation of the numbers are $$\begin{gathered} 3^{2.2}=11.212 \\ {3}^{2.23}=11.587 \\ {3}^{2.236}=11.664 \\ {3}^{\sqrt{5}}=11.665 \end{gathered}$$

Part (a) Step 1. Given

The function $3^{2.2}$

To approximate the value.

Part (a) Step 2. Use the calculator and evaluate

By using calculator,

$$\begin{gathered} 3^{2.2}=11.2115 \\ =11.212 \end{gathered}$$

Part (b) Step 1. Given

The function $3^{2.23}$

To approximate the value.

Part (b) Step 2. Use the calculator and evaluate

By using the calculator,

$$\begin{gathered} 3^{2.23}=11.5872505 \\ =11.587 \end{gathered}$$

Part (c) Step 1. Given

The function $3^{2.236}$

To approximate the value.

Part (c) Step 2. Use the calculator and evaluate

By using the calculator,

$$\begin{gathered} 3^{2.236}=11.66388221 \\ =11.664 \end{gathered}$$

Part (d) Step 1. Given

The function $3^{\sqrt{5}}$

To approximate the value.

Part (d) Step 2. Use the calculator and evaluate

By using the calculator,

$$\begin{gathered} 3^{\sqrt{5}}=3^{2.2361} \\ =11.6651636 \\ =11.665 \end{gathered}$$