In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^2.3

Verified step by step guidance

1. Identify the expression to approximate: \(e^{2.3}\), where \(e\) is the base of the natural logarithm, approximately equal to 2.71828.
2. Use a calculator to evaluate the exponential function \(e^{2.3}\). Most scientific calculators have an \(\texttt{exp}\) or \(\texttt{e^x}\) button for this purpose.
3. Enter the value 2.3 as the exponent into the calculator after pressing the \(e^x\) or equivalent button.
4. Calculate the value and obtain the decimal approximation from the calculator display.
5. Round the result to three decimal places by looking at the fourth decimal digit and adjusting the third decimal digit accordingly.

Key Concepts

Exponential Function

An exponential function involves a constant base raised to a variable exponent, commonly written as e^x, where e is Euler's number (~2.718). It models growth or decay processes and is fundamental in algebra and calculus.

Use of a Calculator for Approximation

Calculators can compute values of functions like e^x that are difficult to calculate by hand. Using a calculator allows for quick and accurate approximation of such expressions to a desired decimal precision.

Rounding to a Specified Decimal Place

Rounding involves adjusting a number to a certain number of decimal places for simplicity or clarity. Here, answers are rounded to three decimal places, meaning the value is truncated or increased based on the fourth decimal digit.