Finite Math Examples

$f = 18 {(0.985)}^{t}$

Step 1

Rewrite the equation as $18 \cdot {0.985}^{t} = f$ .

$18 \cdot {0.985}^{t} = f$

Step 2

Divide each term in $18 \cdot {0.985}^{t} = f$ by $18$ and simplify.

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Step 2.1

Divide each term in $18 \cdot {0.985}^{t} = f$ by $18$ .

$\frac{18 \cdot {0.985}^{t}}{18} = \frac{f}{18}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $18$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{18 \cdot {0.985}^{t}}{18} = \frac{f}{18}$

Step 2.2.1.2

Divide ${0.985}^{t}$ by $1$ .

${0.985}^{t} = \frac{f}{18}$

Step 3

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

$\ln ({0.985}^{t}) = \ln (\frac{f}{18})$

Step 4

Expand $\ln ({0.985}^{t})$ by moving $t$ outside the logarithm.

$t \ln (0.985) = \ln (\frac{f}{18})$

Step 5

Divide each term in $t \ln (0.985) = \ln (\frac{f}{18})$ by $\ln (0.985)$ and simplify.

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Step 5.1

Divide each term in $t \ln (0.985) = \ln (\frac{f}{18})$ by $\ln (0.985)$ .

$\frac{t \ln (0.985)}{\ln (0.985)} = \frac{\ln (\frac{f}{18})}{\ln (0.985)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (0.985)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{t \ln (0.985)}{\ln (0.985)} = \frac{\ln (\frac{f}{18})}{\ln (0.985)}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{f}{18})}{\ln (0.985)}$