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To determine the number of years it takes for the population of wild boars to reach 305, we need to solve the logistic model equation for \( t \) when \( P(t) = 305 \). 

The logistic model given is:

\[ P(t) = \frac{750}{1 + 24e^{-0.4t}} \]

We want to find \( t \) when \( P(t) = 305 \):

\[ 305 = \frac{750}{1 + 24e^{-0.4t}} \]

Let's solve for \( t \):

1. First, multiply both sides by the denominator to get rid of the fraction:
\[ 305 \left(1 + 24e^{-0.4t}\right) = 750 \]

2. Expand and isolate the exponential term:
\[ 305 + 7320e^{-0.4t} = 750 \]
\[ 7320e^{-0.4t} = 750 - 305 \]
\[ 7320e^{-0.4t} = 445 \]

3. Divide both sides by 7320:
\[ e^{-0.4t} = \frac{445}{7320} \]
\[ e^{-0.4t} = \frac{445}{7320} \approx 0.0608 \]

4. Take the natural logarithm (ln) of both sides to solve for \( t \):
\[ -0.4t = \ln(0.0608) \]
\[ -0.4t = -2.799 \]

5. Divide by -0.4 to isolate \( t \):
\[ t = \frac{-2.799}{-0.4} \]
\[ t = 7 \]

Therefore, it takes approximately 7 years for the population to reach 305 wild boars.

Would you like more details or have any questions? Here are some questions you can ask next:

1. Can you explain how to derive the logistic model equation?
2. What are other real-world applications of logistic growth models?
3. How would the model change if the initial population was different?
4. What assumptions are made in a logistic growth model?
5. How does the value of the growth rate affect the population growth?

**Tip:** When working with logistic growth models, always check the asymptotic behavior to understand the long-term trends of the population.

Explore how to solve the logistic growth model equation for wild boar population dynamics, determining the time required for the population to reach 305. This problem involves exponential functions, natural logarithms, and applications of mathematical modeling in biology.

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