Use the ALEKS calculator to evaluate each expression. Round your answers to the nearest thousandth. Do not round any intermediate computations.

[tex]\[
\begin{array}{r}
215 e^{0.55} = \square \\
e^{-0.2} = \square
\end{array}
\][/tex]



Answer :

Let's evaluate each expression step-by-step.

1. Evaluate [tex]\( 215 e^{0.55} \)[/tex]:

a. First, identify the constant [tex]\( e \)[/tex]. In mathematics, [tex]\( e \)[/tex] (Euler's number) is approximately 2.71828.

b. Next, we will raise [tex]\( e \)[/tex] to the power of 0.55:
[tex]\[ e^{0.55} \][/tex]

c. Using the scientific constant [tex]\( e \approx 2.71828 \)[/tex], raising it to the 0.55 power yields a value. When calculated, this value is approximately:
[tex]\[ e^{0.55} \approx 1.733 \][/tex]

d. Now, multiply the result by 215:
[tex]\[ 215 \times 1.733 \approx 372.649 \][/tex]

e. Finally, when rounding to the nearest thousandth, the answer remains:
[tex]\[ 215 e^{0.55} \approx 372.649 \][/tex]

2. Evaluate [tex]\( e^{-0.2} \)[/tex]:

a. Similarly, for the expression [tex]\( e^{-0.2} \)[/tex]:

b. Raise [tex]\( e \)[/tex] to the power of -0.2:
[tex]\[ e^{-0.2} \][/tex]

c. Using the constant [tex]\( e \)[/tex], the calculation provides an approximate value of:
[tex]\[ e^{-0.2} \approx 0.819 \][/tex]

d. No further multiplication is needed here. Upon rounding it to the nearest thousandth, the answer is:
[tex]\[ e^{-0.2} \approx 0.819 \][/tex]

To summarize, the rounded results for the given expressions are:
[tex]\[ 215 e^{0.55} \approx 372.649 \][/tex]
[tex]\[ e^{-0.2} \approx 0.819 \][/tex]