Precalculus Examples

$a = 16 e^{- 0.00012 t \cdot 8220}$

Step 1

Simplify.

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Step 1.1

Multiply $8220$ by $- 0.00012$ .

$a = 16 e^{- 0.9864 t}$

Step 1.2

Divide each term in $a = 16 e^{- 0.9864 t}$ by $16$ .

$\frac{a}{16} = \frac{16 e^{- 0.9864 t}}{16}$

Step 1.3

Reduce by cancelling the common factors.

$\frac{a}{16} = e^{- 0.9864 t}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(\frac{a}{16})$ equals the exponent $(- 0.9864 t)$ .

$\log_{e} (\frac{a}{16}) = - 0.9864 t$