Question

use the aleks calculator to evaluate each expression. round your answers to the nearest thousandth. do not round any intermediate computations.
$e^{-0.25}=\square$
$175e^{0.5}=\square$

Explanation:

Step1: Evaluate \( e^{-0.25} \)

Using the ALEKS calculator or the formula for exponential function, \( e^{-0.25} \) is calculated. \( e^{-0.25} \approx 0.7788007830714049 \). Rounding to the nearest thousandth, we look at the fourth decimal place. The fourth decimal is 8, which is greater than or equal to 5, so we round up the third decimal. So \( e^{-0.25} \approx 0.779 \).

Step2: Evaluate \( 175e^{0.5} \)

First, calculate \( e^{0.5} \approx 1.6487212707001281 \). Then multiply by 175: \( 175 \times 1.6487212707001281 = 175 \times 1.6487212707001281 \approx 288.5262223725224 \). Rounding to the nearest thousandth, we look at the fourth decimal place. The fourth decimal is 2, which is less than 5, so we keep the third decimal as is. So \( 175e^{0.5} \approx 288.526 \).

Answer:

\( e^{-0.25} \approx \boxed{0.779} \)
\( 175e^{0.5} \approx \boxed{288.526} \)