Finite Math Examples

$58000 = 21000 e^{r (20)}$

Step 1

Rewrite the equation as $21000 e^{r (20)} = 58000$ .

$21000 e^{r (20)} = 58000$

Step 2

Divide each term in $21000 e^{r (20)} = 58000$ by $21000$ and simplify.

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Step 2.1

Divide each term in $21000 e^{r (20)} = 58000$ by $21000$ .

$\frac{21000 e^{r (20)}}{21000} = \frac{58000}{21000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $21000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{21000 e^{r (20)}}{21000} = \frac{58000}{21000}$

Step 2.2.1.2

Divide $e^{r (20)}$ by $1$ .

$e^{r (20)} = \frac{58000}{21000}$

Step 2.2.2

Move $20$ to the left of $r$ .

$e^{20 r} = \frac{58000}{21000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $58000$ and $21000$ .

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Step 2.3.1.1

Factor $1000$ out of $58000$ .

$e^{20 r} = \frac{1000 (58)}{21000}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $1000$ out of $21000$ .

$e^{20 r} = \frac{1000 \cdot 58}{1000 \cdot 21}$

Step 2.3.1.2.2

Cancel the common factor.

$e^{20 r} = \frac{1000 \cdot 58}{1000 \cdot 21}$

Step 2.3.1.2.3

Rewrite the expression.

$e^{20 r} = \frac{58}{21}$

Step 3

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{20 r}) = \ln (\frac{58}{21})$

Step 4

Expand the left side.

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Step 4.1

Expand $\ln (e^{20 r})$ by moving $20 r$ outside the logarithm.

$20 r \ln (e) = \ln (\frac{58}{21})$

Step 4.2

The natural logarithm of $e$ is $1$ .

$20 r \cdot 1 = \ln (\frac{58}{21})$

Step 4.3

Multiply $20$ by $1$ .

$20 r = \ln (\frac{58}{21})$

Step 5

Divide each term in $20 r = \ln (\frac{58}{21})$ by $20$ and simplify.

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Step 5.1

Divide each term in $20 r = \ln (\frac{58}{21})$ by $20$ .

$\frac{20 r}{20} = \frac{\ln (\frac{58}{21})}{20}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $20$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{20 r}{20} = \frac{\ln (\frac{58}{21})}{20}$

Step 5.2.1.2

Divide $r$ by $1$ .

$r = \frac{\ln (\frac{58}{21})}{20}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = \frac{\ln (\frac{58}{21})}{20}$

Decimal Form:

$r = 0.05079602 \dots$