Precalculus Examples

$q (6) = 6 (1 - e^{- 0.05 t})$

Step 1

Simplify.

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Step 1.1

Divide each term in $q (6) = 6 (1 - e^{- 0.05 t})$ by $6$ .

$\frac{q (6)}{6} = \frac{6 (1 - e^{- 0.05 t})}{6}$

Step 1.2

Move $6$ to the left of $q$ .

$\frac{6 q}{6}$

Step 1.3

Cancel the common factor of $6$ .

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Step 1.3.1

Cancel the common factor.

$\frac{6 q}{6}$

Step 1.3.2

Divide $q$ by $1$ .

$q$

Step 1.4

Reduce by cancelling the common factors.

$q = e^{- 0.05 t}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(q)$ equals the exponent $(- 0.05 t)$ .

$\log_{e} (q) = - 0.05 t$