Precalculus Examples

$x = 4 e^{t}$ , $y = 3 e^{- 2 t}$

Step 1

Solve the equation for $e$ .

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Step 1.1

Rewrite the equation as $4 e^{t} = x$ .

$4 e^{t} = x$

$y = 3 e^{- 2 t}$

Step 1.2

Subtract $4 e^{t}$ from both sides of the equation.

$0 = x - 4 e^{t}$

$y = 3 e^{- 2 t}$

Step 1.3

Rewrite the equation as $x - 4 e^{t} = 0$ .

$x - 4 e^{t} = 0$

$y = 3 e^{- 2 t}$

$x - 4 e^{t} = 0$

$y = 3 e^{- 2 t}$

Step 2

Simplify the right side.

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Step 2.1

Remove parentheses.

$y = 3 \cdot 0^{- 2 t}$

$x - 4 e^{t} = 0$

$y = 3 \cdot 0^{- 2 t}$

$x - 4 e^{t} = 0$