Finite Math Examples

$5000 {(1 + \frac{0.075}{4})}^{4 t} = 7300$

Step 1

Simplify.

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Step 1.1

Divide $0.075$ by $4$ .

$5000 {(1 + 0.01875)}^{4 t} = 7300$

Step 1.2

Add $1$ and $0.01875$ .

$5000 \cdot {1.01875}^{4 t} = 7300$

Step 2

Divide each term in $5000 \cdot {1.01875}^{4 t} = 7300$ by $5000$ and simplify.

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Step 2.1

Divide each term in $5000 \cdot {1.01875}^{4 t} = 7300$ by $5000$ .

$\frac{5000 \cdot {1.01875}^{4 t}}{5000} = \frac{7300}{5000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5000 \cdot {1.01875}^{4 t}}{5000} = \frac{7300}{5000}$

Step 2.2.1.2

Divide ${1.01875}^{4 t}$ by $1$ .

${1.01875}^{4 t} = \frac{7300}{5000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $7300$ and $5000$ .

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Step 2.3.1.1

Factor $100$ out of $7300$ .

${1.01875}^{4 t} = \frac{100 (73)}{5000}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $100$ out of $5000$ .

${1.01875}^{4 t} = \frac{100 \cdot 73}{100 \cdot 50}$

Step 2.3.1.2.2

Cancel the common factor.

${1.01875}^{4 t} = \frac{100 \cdot 73}{100 \cdot 50}$

Step 2.3.1.2.3

Rewrite the expression.

${1.01875}^{4 t} = \frac{73}{50}$

Step 3

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

$\ln ({1.01875}^{4 t}) = \ln (\frac{73}{50})$

Step 4

Expand $\ln ({1.01875}^{4 t})$ by moving $4 t$ outside the logarithm.

$4 t \ln (1.01875) = \ln (\frac{73}{50})$

Step 5

Divide each term in $4 t \ln (1.01875) = \ln (\frac{73}{50})$ by $4 \ln (1.01875)$ and simplify.

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Step 5.1

Divide each term in $4 t \ln (1.01875) = \ln (\frac{73}{50})$ by $4 \ln (1.01875)$ .

$\frac{4 t \ln (1.01875)}{4 \ln (1.01875)} = \frac{\ln (\frac{73}{50})}{4 \ln (1.01875)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 t \ln (1.01875)}{4 \ln (1.01875)} = \frac{\ln (\frac{73}{50})}{4 \ln (1.01875)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{t \ln (1.01875)}{\ln (1.01875)} = \frac{\ln (\frac{73}{50})}{4 \ln (1.01875)}$

Step 5.2.2

Cancel the common factor of $\ln (1.01875)$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{t \ln (1.01875)}{\ln (1.01875)} = \frac{\ln (\frac{73}{50})}{4 \ln (1.01875)}$

Step 5.2.2.2

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{73}{50})}{4 \ln (1.01875)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\ln (\frac{73}{50})}{4 \ln (1.01875)}$

Decimal Form:

$t = 5.09297724 \dots$