Precalculus Examples

$f (10) = 800 e^{- 0.0245 \cdot 10}$

Step 1

Simplify.

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Step 1.1

Multiply

$- 0.0245$ by

$10$ .

$f (10) = 800 e^{- 0.245}$

Step 1.2

Divide each term in

$f (10) = 800 e^{- 0.245}$ by

$800$ .

$\frac{f (10)}{800} = \frac{800 e^{- 0.245}}{800}$

Step 1.3

Move

$10$ to the left of

$f$ .

$\frac{10 f}{800}$

Step 1.4

Cancel the common factor of

$10$ and

$800$ .

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Step 1.4.1

Factor

$10$ out of

$10 f$ .

$\frac{10 (f)}{800}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor

$10$ out of

$800$ .

$\frac{10 f}{10 \cdot 80}$

Step 1.4.2.2

Cancel the common factor.

$\frac{10 f}{10 \cdot 80}$

Step 1.4.2.3

Rewrite the expression.

$\frac{f}{80}$

Step 1.5

Reduce by cancelling the common factors.

$\frac{f}{80} = e^{- 0.245}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base

$(e)$ of the left side

$(\frac{f}{80})$ equals the exponent

$(- 0.245)$ .

$\log_{e} (\frac{f}{80}) = - 0.245$