Question

Give approximate answer to two decimal places.
Evaluate StartFraction 76.514 Over 1 plus 0.839 e Superscript negative 0.0292 left parenthesis 80 right parenthesis EndFraction
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Part 1
StartFraction 76.514 Over 1 plus 0.839 e Superscript negative 0.0292 left parenthesis 80 right parenthesis EndFraction
almost equals
  
enter your response here
​(Do not round until the final answer. Then round to two decimal places as​ needed.)

Answer 1

To evaluate the expression

\[
\frac{76.514}{1 + 0.839 e^{-0.0292 \times 80}}
\]

we will start by calculating \( e^{-0.0292 \times 80} \).

First, calculate \(-0.0292 \times 80\):

\[
-0.0292 \times 80 = -2.336
\]

Next, calculate \( e^{-2.336} \):

\[
e^{-2.336} \approx 0.096
\]

Now substitute this back into the expression:

\[
\frac{76.514}{1 + 0.839 \times 0.096}
\]

Calculate \(0.839 \times 0.096\):

\[
0.839 \times 0.096 \approx 0.080544
\]

Now, substitute this value back into the equation:

\[
\frac{76.514}{1 + 0.080544} = \frac{76.514}{1.080544}
\]

Now perform the division:

\[
76.514 \div 1.080544 \approx 70.83
\]

Finally, rounding to two decimal places, the answer is

\[
\boxed{70.83}
\]