You have the function \( P(8) = 20500 \cdot (1.07)^8 \), and you want to compute the value of this expression.

Let's calculate it:

\[
P(8) = 20500 \cdot (1.07)^8
\]

Now I'll compute the value of \( (1.07)^8 \) and then multiply it by 20500.

\[
(1.07)^8 \approx 1.71819
\]

Multiplying:

\[
P(8) = 20500 \cdot 1.71819 \approx 35222.90
\]

So, the value of \( P(8) \) is approximately **35,222.90**.

Would you like more details on how this was calculated or have any other questions?

Here are 5 related questions:
1. What is the significance of the 7% growth factor in this equation?
2. How would the value change if the exponent was 10 instead of 8?
3. How can we interpret the meaning of \( P(t) = 20500 \cdot (1.07)^t \) in real-world scenarios?
4. What would happen if the growth rate was compounded continuously instead of annually?
5. How does changing the initial value (20500) affect the function?

**Tip:** In exponential functions, small changes in the exponent or the base can lead to large differences in the output, so always check these values carefully!

Discover how to solve the exponential growth function P(8) = 20500 ⋅ (1.07)^8 with step-by-step guidance. This solution shows the significance of a 7% growth factor, exponentiation, and how changing values impacts the outcome. Ideal for students in Grades 9-12.

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