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

\[
300000 = 111810.84(1 + r)^6
\]

we will go through the following steps:

### Step 1: Isolate the exponential term
First, divide both sides of the equation by 111810.84:

\[
\frac{300000}{111810.84} = (1 + r)^6
\]

Calculating the left-hand side:

\[
\frac{300000}{111810.84} \approx 2.682
\]

So, the equation becomes:

\[
2.682 = (1 + r)^6
\]

### Step 2: Remove the exponent
To eliminate the exponent, take the sixth root (or raise both sides to the power of \( \frac{1}{6} \)):

\[
(2.682)^{\frac{1}{6}} = 1 + r
\]

### Step 3: Solve for \( r \)
Now, calculate \( (2.682)^{\frac{1}{6}} \):

\[
(2.682)^{\frac{1}{6}} \approx 1.1797
\]

Finally, solve for \( r \):

\[
r = 1.1797 - 1 = 0.1797
\]

### Conclusion:
The value of \( r \) is approximately \( 0.1797 \), or 17.97%.

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would the equation change if the exponent were 7 instead of 6?
2. What is the significance of the value \( r \) in financial calculations?
3. Can you solve for \( r \) using logarithms?
4. How would the value of \( r \) change if the initial amount were larger or smaller?
5. How does the compound interest formula relate to this equation?

**Tip:** When solving for exponents, logarithms can be a helpful tool if the exponent is not easily simplified.

Learn how to solve the exponential equation 300000 = 111810.84(1+r)^6 step-by-step. This problem involves compound interest and exponential equations, suitable for advanced high school students.

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