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!