Give approximate answer to two decimal places.

Question

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
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​(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

\[ \boxed{70.83} \]