Finite Math Examples

$f (28) = \frac{90}{1 + 271 e^{- 0.122 x}}$

Step 1

Replace the variable $x$ with $28$ in the expression.

$f (28) = \frac{90}{1 + 271 e^{- 0.122 \cdot 28}}$

Step 2

Simplify the result.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

Multiply $- 0.122$ by $28$ .

$f (28) = \frac{90}{1 + 271 e^{- 3.416}}$

Step 2.1.2

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

$f (28) = \frac{90}{1 + 271 (\frac{1}{e^{3.416}})}$

Step 2.1.3

Combine $271$ and $\frac{1}{e^{3.416}}$ .

$f (28) = \frac{90}{1 + \frac{271}{e^{3.416}}}$

Step 2.1.4

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

$f (28) = \frac{90}{\frac{e^{3.416}}{e^{3.416}} + \frac{271}{e^{3.416}}}$

Step 2.1.5

Combine the numerators over the common denominator.

$f (28) = \frac{90}{\frac{e^{3.416} + 271}{e^{3.416}}}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$f (28) = 90 (\frac{e^{3.416}}{e^{3.416} + 271})$

Step 2.3

Combine $90$ and $\frac{e^{3.416}}{e^{3.416} + 271}$ .

$f (28) = \frac{90 e^{3.416}}{e^{3.416} + 271}$

Step 2.4

The final answer is $\frac{90 e^{3.416}}{e^{3.416} + 271}$ .

$\frac{90 e^{3.416}}{e^{3.416} + 271}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{90 e^{3.416}}{e^{3.416} + 271}$

Decimal Form:

$9.09035709 \dots$

Step 4