Precalculus Examples

$0.5 = \frac{12}{10} \cdot (1 - e^{- \frac{10}{5} t})$

Step 1

Simplify.

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Step 1.1

Simplify both sides of the equation.

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Step 1.1.1

Combine $t$ and $\frac{10}{5}$ .

$0.5 = \frac{12}{10} \cdot (1 - e^{- \frac{t \cdot 10}{5}})$

Step 1.1.2

Move $10$ to the left of $t$ .

$0.5 = \frac{12}{10} \cdot (1 - e^{- \frac{10 \cdot t}{5}})$

Step 1.1.3

Multiply $10$ by $t$ .

$0.5 = \frac{12}{10} \cdot (1 - e^{- \frac{10 t}{5}})$

Step 1.2

Multiply each term in $0.5 = \frac{12}{10} \cdot (1 - e^{- \frac{10 t}{5}})$ by $12$ .

$0.5 \cdot 12 = \frac{12}{10} \cdot (1 - e^{- \frac{10 t}{5}}) \cdot 12$

Step 1.3

Multiply $0.5$ by $12$ .

$6$

Step 1.4

Reduce by cancelling the common factors.

$6 = e^{- \frac{10 t}{5}}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(6)$ equals the exponent $(- \frac{10 t}{5})$ .

$\log_{e} (6) = - \frac{10 t}{5}$