Q. 19 - Precalculus Enhanced with Graphing Utilities

Question

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

(a) $3.1^{2.7}$

(b) $3.{14}^{2.71}$

(c) $3.{141}^{2.718}$

(d) ${\mathrm{\pi }}^{\mathrm{e}}$

Step-by-Step Solution

Answer

(a) $21.217$

(b) $22.217$

(c) $22.440$

(d) $22.459$

Part (a) Step 1. Given

Given expression 

$3.1^{2.7}$

Part (a) Step 2. Calculation

on calculating using calculator we get 

$3.1^{2.7\approx }21.216638$

on rounding it off up to three decimal places we get

$3.1^{2.7}\approx 21.216$

Part (b) Step 1. Given

Given expression

$3.{14}^{2.71}$

Part (b) Step 2. Calculation

on calculating using calculator we get 

$3.{14}^{2.71}\approx 22.216689$

on rounding it off up to three decimal places we get

$3.{14}^{2.71}\approx 22.216$

Part (c) Step 1. Given

Given expression

$3.{141}^{2.718}$

Part (c) Step 2. Calculation

on calculating using calculator we get 

$3.{141}^{2.718}\approx 22.440402$

on rounding it off up to three decimal places we get

$3.{141}^{2.718}\approx 22.440$

Part (d) Step 1. Given

Given expression

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

Part (d) Step 2. Calculation

on calculating using calculator we get 

${\mathrm{\pi }}^{\mathrm{e}}\approx 22.459157$

on rounding it off up to three decimal places we get

${\mathrm{\pi }}^{\mathrm{e}}\approx 22.459$