Q. 20 - Precalculus Enhanced with Graphing Utilities

Question

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

(a) $2.7^{3.1}$

(b) $2.{71}^{3.14}$

(c) $2.{718}^{3.141}$

(d) $e^{\mathrm{\pi }}$

Step-by-Step Solution

Answer

(a) $21.738$

(b) $22.884$

(c) $23.119$

(d) $23.141$

Part (a) Step 1. Given

Given expression 

$2.7^{3.1}$

Part (a) Step 2. Calculation

on calculating using calculator we get 

$2.7^{3.1}\approx 21.738404$

on rounding it off up to three decimal places we get

$2.7^{3.1}\approx 21.738$

Part (b) Step 1. Given

Given expression

$2.{71}^{3.14}$

Part (b) Step 2. Calculation

on calculating using calculator we get 

$2.{71}^{3.14}\approx 22.883559$

on rounding it off up to three decimal places we get

$2.{71}^{3.14}\approx 22.883$

Part (c) Step 1. Given

Given expression

$2.{718}^{3.141}$

Part (c) Step 2. Calculation

on calculating using calculator we get 

$2.{718}^{3.141}\approx 23.1194516$

on rounding it off up to three decimal places we get

$2.{718}^{3.141}\approx 23.119$

Part (d) Step 1. Given

Given expression

$e^{\mathrm{\pi }}$

Part (d) Step 2. Calculation

on calculating using calculator we get 

$e^{\mathrm{\pi }}\approx 23.14069$

on rounding it off up to three decimal places we get

$e^{\mathrm{\pi }}\approx 23.140$