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To solve for \( t \) in the equation:

\[
400 \cdot (1.06)^t = 1600
\]

we can follow these steps:

1. Divide both sides by 400:
   \[
   (1.06)^t = \frac{1600}{400} = 4
   \]

2. Take the natural logarithm of both sides to bring down the exponent:
   \[
   \ln((1.06)^t) = \ln(4)
   \]

3. Use the power rule of logarithms:
   \[
   t \cdot \ln(1.06) = \ln(4)
   \]

4. Solve for \( t \) by dividing:
   \[
   t = \frac{\ln(4)}{\ln(1.06)}
   \]

5. Using a calculator, approximate:
   \[
   t \approx \frac{1.3863}{0.0583} \approx 23.78
   \]

**Answer:**
\[
t \approx 23.78
\]

Solve the equation 400 * (1.06)^t = 1600 for t. Round your answer to two decimal places.

Learn how to solve the exponential equation 400 * (1.06)^t = 1600 by isolating t using logarithmic properties. This detailed solution includes step-by-step calculations and is ideal for students in Grades 10-12.

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