Calculus Examples

$F (t) = 2 \frac{1}{2^{3 t}}$

Step 1

Combine $2$ and $\frac{1}{2^{3 t}}$ .

$F t = \frac{2}{2^{3 t}}$

Step 2

Divide each term in $F t = \frac{2}{2^{3 t}}$ by $t$ and simplify.

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Step 2.1

Divide each term in $F t = \frac{2}{2^{3 t}}$ by $t$ .

$\frac{F t}{t} = \frac{\frac{2}{2^{3 t}}}{t}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $t$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{F t}{t} = \frac{\frac{2}{2^{3 t}}}{t}$

Step 2.2.1.2

Divide $F$ by $1$ .

$F = \frac{\frac{2}{2^{3 t}}}{t}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$F = \frac{2}{2^{3 t}} \cdot \frac{1}{t}$

Step 2.3.2

Combine.

$F = \frac{2 \cdot 1}{2^{3 t} t}$

Step 2.3.3

Simplify the expression.

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Step 2.3.3.1

Multiply $2$ by $1$ .

$F = \frac{2}{2^{3 t} t}$

Step 2.3.3.2

Reorder factors in $\frac{2}{2^{3 t} t}$ .

$F = \frac{2}{t \cdot 2^{3 t}}$

Step 3

To rewrite as a function of $t$ , write the equation so that $F$ is by itself on one side of the equal sign and an expression involving only $t$ is on the other side.

$f (t) = \frac{2}{t \cdot 2^{3 t}}$