Question

use the aleks calculator to evaluate each expression. round your answers to the nearest thousandth. do not round any intermediate computations. $e^{0.8}=square$ $250e^{-0.85}=square$

Explanation:

Step1: Evaluate \( e^{0.8} \)

Using a calculator, we know that \( e \approx 2.71828 \). Calculate \( e^{0.8} \). \( e^{0.8} \approx 2.225540928492468 \). Rounding to the nearest thousandth (three decimal places), we look at the fourth decimal place, which is 5. So we round up the third decimal place. \( 2.225540928492468 \approx 2.226 \).

Step2: Evaluate \( 250e^{-0.85} \)

First, calculate \( e^{-0.85} \). \( e^{-0.85}=\frac{1}{e^{0.85}} \). \( e^{0.85} \approx 2.339646961536732 \), so \( e^{-0.85} \approx \frac{1}{2.339646961536732} \approx 0.4274029197128237 \). Then multiply by 250: \( 250\times0.4274029197128237 = 106.85072992820592 \). Rounding to the nearest thousandth, we look at the fourth decimal place, which is 7. So we round up the third decimal place. \( 106.85072992820592 \approx 106.851 \).

Answer:

\( e^{0.8} \approx \boxed{2.226} \)
\( 250e^{-0.85} \approx \boxed{106.851} \)