Find *P*:

30,000 = *P*(1 + 0.04)48.

(Round your answer to two decimal places

We are given the equation:

\[
30,000 = P(1 + 0.04)^{48}
\]

This is an exponential equation where we are solving for \( P \), which represents the principal amount. Let's break this down step by step:

1. Simplify the expression inside the parentheses:
   \[
   1 + 0.04 = 1.04
   \]
   
   So the equation becomes:
   \[
   30,000 = P(1.04)^{48}
   \]

2. Calculate \( (1.04)^{48} \).

3. Divide both sides of the equation by \( (1.04)^{48} \) to solve for \( P \).

Let's proceed with the calculations.The value of \( P \), rounded to two decimal places, is approximately:

\[
P \approx 4565.84
\]

This represents the principal amount before the growth over 48 periods at a 4% rate.

Would you like further details on this process, or do you have any other questions?

Here are 5 related questions for deeper understanding:
1. How does changing the interest rate affect the principal \( P \)?
2. What happens to the principal if the number of periods increases?
3. Can you find the future value if the principal is known and the interest rate changes?
4. How is compound interest different from simple interest in these calculations?
5. What does the exponent in the formula represent in real-world financial situations?

**Tip:** When solving for \( P \) in exponential growth formulas, always isolate the exponential part first by simplifying, then proceed to solve step by step.

Find P: 30,000 = P(1 + 0.04)^48. (Round your answer to two decimal places)

Discover how to solve the exponential equation 30,000 = P(1.04)^48 step-by-step. This problem involves calculating the principal (P) in an exponential growth scenario with a 4% interest rate over 48 periods. Suitable for students in Grades 9-12.

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