Precalculus Examples

$50000 = 5000 (10^{0.5 t})$

Step 1

Rewrite the equation as $5000 \cdot 10^{0.5 t} = 50000$ .

$5000 \cdot 10^{0.5 t} = 50000$

Step 2

Divide each term in $5000 \cdot 10^{0.5 t} = 50000$ by $5000$ and simplify.

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Step 2.1

Divide each term in $5000 \cdot 10^{0.5 t} = 50000$ by $5000$ .

$\frac{5000 \cdot 10^{0.5 t}}{5000} = \frac{50000}{5000}$

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.

$\frac{5000 \cdot 10^{0.5 t}}{5000} = \frac{50000}{5000}$

Step 2.2.1.2

Divide $10^{0.5 t}$ by $1$ .

$10^{0.5 t} = \frac{50000}{5000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $50000$ by $5000$ .

$10^{0.5 t} = 10$

Step 3

Create equivalent expressions in the equation that all have equal bases.

$10^{0.5 t} = 10^{1}$

Step 4

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$0.5 t = 1$

Step 5

Divide each term in $0.5 t = 1$ by $0.5$ and simplify.

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Step 5.1

Divide each term in $0.5 t = 1$ by $0.5$ .

$\frac{0.5 t}{0.5} = \frac{1}{0.5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $0.5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{0.5 t}{0.5} = \frac{1}{0.5}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{1}{0.5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $1$ by $0.5$ .

$t = 2$