Given P ( t )

To evaluate $P(3)$, substitute $t = 3$ into the given function:

$P(t) = 18 \cdot (2.3)^t$

$P(3) = 18 \cdot (2.3)^3$

First, calculate $(2.3)^3$:

$2.3^3 = 2.3 \cdot 2.3 \cdot 2.3 = 12.167$

Now multiply:

$P(3) = 18 \cdot 12.167 = 219.006$

Round to the nearest whole number:

$P(3) \approx 219$

Final Answer:

$P(3) = 219$

---

Would you like a detailed explanation of any of the steps?

Here are 5 related questions you might find helpful:

1. How do you calculate powers of decimals?
2. Why is rounding important, and how do you round correctly?
3. What are other examples of exponential functions in real-world applications?
4. How can the base of an exponential function affect its growth rate?
5. What happens to $P(t)$ as $t \to \infty$ in this function?

Tip: Always double-check your calculations when working with powers and large numbers to avoid errors.