Let's address each part of the problem one by one:

Part 1: Carrying Capacity

The carrying capacity is already identified as 1000 grams, which is the maximum value of $P(t)$ when $t \to \infty$.

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Part 2: Growth Rate

The growth rate is given as $r = 0.449$, which translates to 44.9% per hour.

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Part 3: Graphing the Model

The graph represents logistic growth, starting at a low population, increasing rapidly during the growth phase, and leveling off near the carrying capacity (1000 grams). You can plot the function in the specified range: $P(t) = \frac{1000}{1 + 30.42e^{-0.449t}}$ Given $X_{\text{min}} = 0, X_{\text{max}} = 20, Y_{\text{min}} = 0, Y_{\text{max}} = 1000$, the curve should match the description provided.

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Part 4: Population After 5 Hours

The population at $t = 5$ is calculated using the given logistic growth model: $P(5) = \frac{1000}{1 + 30.42e^{-0.449 \cdot 5}}$

1. Compute $e^{-0.449 \cdot 5}$: $-0.449 \cdot 5 = -2.245, \quad e^{-2.245} \approx 0.106$

2. Calculate the denominator: $1 + 30.42 \cdot 0.106 \approx 1 + 3.224 = 4.224$

3. Find $P(5)$: $P(5) = \frac{1000}{4.224} \approx 236.8 \, \text{grams}$

Thus, the population after 5 hours is approximately 236.8 grams.

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Part 5: Additional Questions to Expand Understanding

1. How does the logistic growth model differ from exponential growth in long-term population prediction?
2. What happens to the rate of growth as $t \to \infty$ in this logistic model?
3. Can the growth rate of 44.9% per hour remain consistent indefinitely in the real world? Why or why not?
4. How sensitive is the population prediction to changes in the initial population size (e.g., $P(0)$)?
5. What does the parameter $30.42$ represent in the context of the logistic model?

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Tip: In logistic growth, the population grows rapidly initially but slows down as it approaches the carrying capacity due to limited resources. This is a key difference from exponential growth.