Question

evaluate the expression to four decimal places, using a calculator.
$e^{-2.5}=\square$
question help: \\( \square \\) video \\( \square \\) ebook

Explanation:

Step1: Recall the value of \(e\)

\(e\approx2.71828\)

Step2: Calculate \(e^{-2.5}\)

Using the formula \(a^{-n}=\frac{1}{a^{n}}\), so \(e^{-2.5}=\frac{1}{e^{2.5}}\)
\(e^{2.5}=e^{2 + 0.5}=e^{2}\times e^{0.5}\)
\(e^{2}\approx7.3891\), \(e^{0.5}\approx1.6487\)
\(e^{2.5}\approx7.3891\times1.6487\approx12.1825\)
\(e^{-2.5}=\frac{1}{e^{2.5}}\approx\frac{1}{12.1825}\approx0.0820\)
(Alternatively, directly use a calculator: input \(\text{exp}(- 2.5)\) on a scientific calculator)

Answer:

\(0.0821\) (using a calculator for more accurate result: when calculating \(e^{-2.5}\) with a calculator, \(e^{-2.5}\approx0.082085\approx0.0821\) to four decimal places)