Question

use the aleks calculator to evaluate each expression. round your answers to the nearest thousandth. do not round any intermediate computations.
$e^{-0.2}=\square$
$230e^{0.35}=\square$

Explanation:

Step1: Evaluate \( e^{-0.2} \)

Using a calculator, we know that \( e \approx 2.71828 \). Calculate \( e^{-0.2} \) directly. \( e^{-0.2}=\frac{1}{e^{0.2}}\approx\frac{1}{1.22140}\approx0.81873 \). Rounding to the nearest thousandth, we get \( 0.819 \).

Step2: Evaluate \( 230e^{0.35} \)

First, calculate \( e^{0.35}\approx1.41907 \). Then multiply by 230: \( 230\times1.41907 = 230\times1.41907 = 326.3861 \). Rounding to the nearest thousandth, we get \( 326.386 \).

Answer:

\( e^{-0.2}\approx\boxed{0.819} \)
\( 230e^{0.35}\approx\boxed{326.386} \)