Q. 18 - Precalculus Enhanced with Graphing Utilities

Question

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

(a) $2^{2.7}$

(b) $2^{2.71}$

(c) $2^{2.718}$

(d) $2^e$

Step-by-Step Solution

Answer

(a) $6.498$

(b) $6.543$

(c) $6.579$

(d) $6.580$

Part (a) Step 1. Given

Given expression 

$2^{2.7}$

Part (a) Step 2. Calculation

on calculating using calculator we get 

$2^{2.7}\approx 6.4980191$

on rounding it off up to three decimal places we get

$2^{2.7\approx }6.498$

Part (b) Step 1. Given

Given expression

$2^{2.71}$

Part (b) Step 2. Calculation

on calculating using calculator we get 

$2^{2.71}\approx 6.5432164$

on rounding it off up to three decimal places we get

$2^{2.71}\approx 6.543$

Part (c) Step 1. Given

Given expression

$2^{2.718}$

Part (c) Step 2. Calculation

on calculating using calculator we get 

$2^{2.718}\approx 6.5796005$

on rounding it off up to three decimal places we get

$2^{2.718}\approx 6.579$

Part (d) Step 1. Given

Given expression

$2^e$

Part (d) Step 2. Calculation

on calculating using calculator we get 

$2^e\approx 6.580885$

on rounding it off up to three decimal places we get

$2^e\approx 6.580$