Precalculus Examples

$f (10) = 15000 e^{(- 0.05) (10)}$

Step 1

Simplify.

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Step 1.1

Multiply $- 0.05$ by $10$ .

$f (10) = 15000 e^{- 0.5}$

Step 1.2

Divide each term in $f (10) = 15000 e^{- 0.5}$ by $15000$ .

$\frac{f (10)}{15000} = \frac{15000 e^{- 0.5}}{15000}$

Step 1.3

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

$\frac{10 f}{15000}$

Step 1.4

Cancel the common factor of $10$ and $15000$ .

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Step 1.4.1

Factor $10$ out of $10 f$ .

$\frac{10 (f)}{15000}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $10$ out of $15000$ .

$\frac{10 f}{10 \cdot 1500}$

Step 1.4.2.2

Cancel the common factor.

$\frac{10 f}{10 \cdot 1500}$

Step 1.4.2.3

Rewrite the expression.

$\frac{f}{1500}$

Step 1.5

Reduce by cancelling the common factors.

$\frac{f}{1500} = e^{- 0.5}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(\frac{f}{1500})$ equals the exponent $(- 0.5)$ .

$\log_{e} (\frac{f}{1500}) = - 0.5$