Precalculus Examples

$(t) = \frac{500}{1 + 83.3 e^{- 0.162 t}}$

Step 1

Simplify.

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Step 1.1

Multiply each term in $(t) = \frac{500}{1 + 83.3 e^{- 0.162 t}}$ by $500$ .

$(t) \cdot 500 = \frac{500}{1 + 83.3 e^{- 0.162 t}} \cdot 500$

Step 1.2

Move $500$ to the left of $t$ .

$500 t$

Step 1.3

Reduce by cancelling the common factors.

$500 t = e^{- 0.162 t}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(500 t)$ equals the exponent $(- 0.162 t)$ .

$\log_{e} (500 t) = - 0.162 t$