Finite Math Examples

$7000 = 3116.92 {(1 + (\frac{0.039}{4}))}^{4 \cdot t}$

Step 1

Rewrite the equation as $3116.92 {(1 + \frac{0.039}{4})}^{4 \cdot t} = 7000$ .

$3116.92 {(1 + \frac{0.039}{4})}^{4 \cdot t} = 7000$

Step 2

Simplify.

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Step 2.1

Divide $0.039$ by $4$ .

$3116.92 {(1 + 0.00975)}^{4 \cdot t} = 7000$

Step 2.2

Add $1$ and $0.00975$ .

$3116.92 \cdot {1.00975}^{4 \cdot t} = 7000$

Step 3

Divide each term in $3116.92 \cdot {1.00975}^{4 \cdot t} = 7000$ by $3116.92$ and simplify.

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Step 3.1

Divide each term in $3116.92 \cdot {1.00975}^{4 \cdot t} = 7000$ by $3116.92$ .

$\frac{3116.92 \cdot {1.00975}^{4 \cdot t}}{3116.92} = \frac{7000}{3116.92}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3116.92$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3116.92 \cdot {1.00975}^{4 \cdot t}}{3116.92} = \frac{7000}{3116.92}$

Step 3.2.1.2

Divide ${1.00975}^{4 \cdot t}$ by $1$ .

${1.00975}^{4 \cdot t} = \frac{7000}{3116.92}$

${1.00975}^{4 t} = \frac{7000}{3116.92}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $7000$ by $3116.92$ .

${1.00975}^{4 t} = 2.24580675$

Step 4

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

$\ln ({1.00975}^{4 t}) = \ln (2.24580675)$

Step 5

Expand $\ln ({1.00975}^{4 t})$ by moving $4 t$ outside the logarithm.

$4 t \ln (1.00975) = \ln (2.24580675)$

Step 6

Divide each term in $4 t \ln (1.00975) = \ln (2.24580675)$ by $4 \ln (1.00975)$ and simplify.

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Step 6.1

Divide each term in $4 t \ln (1.00975) = \ln (2.24580675)$ by $4 \ln (1.00975)$ .

$\frac{4 t \ln (1.00975)}{4 \ln (1.00975)} = \frac{\ln (2.24580675)}{4 \ln (1.00975)}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $4$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{4 t \ln (1.00975)}{4 \ln (1.00975)} = \frac{\ln (2.24580675)}{4 \ln (1.00975)}$

Step 6.2.1.2

Rewrite the expression.

$\frac{t \ln (1.00975)}{\ln (1.00975)} = \frac{\ln (2.24580675)}{4 \ln (1.00975)}$

Step 6.2.2

Cancel the common factor of $\ln (1.00975)$ .

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Step 6.2.2.1

Cancel the common factor.

$\frac{t \ln (1.00975)}{\ln (1.00975)} = \frac{\ln (2.24580675)}{4 \ln (1.00975)}$

Step 6.2.2.2

Divide $t$ by $1$ .

$t = \frac{\ln (2.24580675)}{4 \ln (1.00975)}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\ln (2.24580675)}{4 \ln (1.00975)}$

Decimal Form:

$t = 20.84622120 \dots$