Q. 17 - Precalculus Enhanced with Graphing Utilities

Question

Approximate each number using a calculator. Express your answer rounded to three decimal places.

(a) $2^{3.14}$

(b) $2^{3.141}$

(c) $2^{3.1415}$

(d) $2^{\mathrm{\pi }}$

Step-by-Step Solution

Answer

(a) $8.815$

(b) $8.821$

(c) $8.824$

(d) $8.825$

 

Part (a) Step 1. Given

Given expression 

$2^{3.14}$

Part (a) Step 2. Calculation

on calculating using calculator we get 

$2^{3.14}\approx 8.8152409270$

on rounding it off up to three decimal places we get

$2^{3.14}\approx 8.815$

Part (b) Step 1. Given

Given expression

$2^{3.141}$ 

Part (b) Step 2. Calculation

on calculating using calculator we get 

$2^{3.141}\approx 8.8213533045$

on rounding it off up to three decimal places we get

$2^{3.141}\approx 8.821$

Part (c) Step 1. Given

Given expression

$2^{3.1415}$

Part (c) Step 2. Calculation

on calculating using calculator we get 

$2^{3.1415}\approx 8.8244110824$

on rounding it off up to three decimal places we get

$2^{3.1415}\approx 8.824$

Part (d) Step 1. Given

Given expression

$2^{\mathrm{\pi }}$

Part (d) Step 2. Calculation

on calculating using calculator we get 

$2^{\mathrm{\pi }}\approx 8.8249778270$

on rounding it off up to three decimal places we get

$2^{\mathrm{\pi }}\approx 8.825$