Evaluate the Function f(3)=8/(1+3e^(-0.7x))

$f (3) = \frac{8}{1 + 3 e^{- 0.7 x}}$

Step 1

Replace the variable $x$ with $3$ in the expression.

$f (3) = \frac{8}{1 + 3 e^{- 0.7 \cdot 3}}$

Step 2

Simplify the result.

Simplify the denominator.

Multiply $- 0.7$ by $3$ .

$f (3) = \frac{8}{1 + 3 e^{- 2.1}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$f (3) = \frac{8}{1 + 3 (\frac{1}{e^{2.1}})}$

Combine $3$ and $\frac{1}{e^{2.1}}$ .

$f (3) = \frac{8}{1 + \frac{3}{e^{2.1}}}$

Write $1$ as a fraction with a common denominator.

$f (3) = \frac{8}{\frac{e^{2.1}}{e^{2.1}} + \frac{3}{e^{2.1}}}$

Combine the numerators over the common denominator.

$f (3) = \frac{8}{\frac{e^{2.1} + 3}{e^{2.1}}}$

Multiply the numerator by the reciprocal of the denominator.

$f (3) = 8 (\frac{e^{2.1}}{e^{2.1} + 3})$

Combine $8$ and $\frac{e^{2.1}}{e^{2.1} + 3}$ .

$f (3) = \frac{8 e^{2.1}}{e^{2.1} + 3}$

The final answer is $\frac{8 e^{2.1}}{e^{2.1} + 3}$ .

$\frac{8 e^{2.1}}{e^{2.1} + 3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{8 e^{2.1}}{e^{2.1} + 3}$

Decimal Form:

$5.85065065 \dots$

Step 4