An initial population of 580 quail increases at a rate of $$ 17 \% $$. It is represented by this formula $$ f(t)=580(1.17)^{t} $$. What is the population after 3 years?

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To determine the population of quail after 3 years, we'll use the exponential growth formula provided:

$$
f(t) = 580 \times (1.17)^t
$$

where:
- $$ f(t) $$ is the population after $$ t $$ years,
- $$ 580 $$ is the initial population,
- $$ 1.17 $$ represents a 17% annual growth rate.

**Step-by-Step Calculation:**

1. **Calculate $$ (1.17)^3 $$:**

$$
1.17^3 = 1.17 \times 1.17 \times 1.17
$$

First, compute $$ 1.17 \times 1.17 $$:

$$
1.17 \times 1.17 = 1.3689
$$

Next, multiply the result by $$ 1.17 $$:

$$
1.3689 \times 1.17 \approx 1.601613
$$

2. **Multiply by the Initial Population:**

$$
f(3) = 580 \times 1.601613 \approx 928.93554
$$

3. **Round to the Nearest Whole Number:**

Since population counts are whole numbers, we'll round $$ 928.93554 $$ to the nearest whole number:

$$
f(3) \approx 929 \text{ quail}
$$

**Conclusion:**

After **3 years**, the quail population is expected to be approximately **929 quail**.
After 3 years, the quail population will be approximately 929 quail.

An initial population of 580 quail increases at a rate of \( 17 \% \). It is represented by this formula \( f(t)=580(1.17)^{t} \). What is the population after 3 years?

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