evaluate the expression to four decimal places, using a calculator.\n$e^{-2.5}=\\square$\nquestion help: \\(…

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)