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]
