In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^-0.95

Verified step by step guidance

1. Identify the expression to evaluate: \(e^{-0.95}\), where \(e\) is the base of the natural logarithm, approximately equal to 2.71828.
2. Recall that \(e^x\) represents the exponential function, which can be calculated using a scientific calculator or a calculator app with an exponential function key.
3. Enter the exponent value \(-0.95\) into the calculator, then use the \(e^x\) function to compute \(e^{-0.95}\).
4. After obtaining the decimal value from the calculator, round the result to three decimal places as instructed.
5. Write down the rounded value as the final approximation of \(e^{-0.95}\).

Key Concepts

Exponential Functions

Exponential functions involve expressions where a constant base is raised to a variable exponent, such as e^x. The number e (approximately 2.718) is a fundamental constant in mathematics, often used in growth and decay models. Understanding how to evaluate e raised to a negative exponent is essential for this problem.

Using a Calculator for Exponentials

Calculators can compute values of exponential expressions like e^x directly, often through a dedicated 'e^x' button. Knowing how to input negative exponents correctly ensures accurate results. This skill is crucial for approximating values that cannot be simplified easily by hand.

Rounding to a Specific Decimal Place

Rounding involves adjusting a number to a specified number of decimal places to simplify or standardize results. For this question, answers must be rounded to three decimal places, meaning the value is truncated or increased based on the fourth decimal digit. Proper rounding ensures clarity and consistency in numerical answers.