To model the situation, we can write the equations representing both the park attendance and the food supply over time.

1. Park Attendance

The attendance is increasing at a rate of 3% per year, so it's an example of exponential growth. The equation for park attendance $A(t)$ after $t$ years is:

$A(t) = A_0 \cdot (1 + r)^t$

where:

• $A_0 = 2$ million people (initial attendance),
• $r = 0.03$ (annual growth rate of 3%),
• $t$ is the number of years.

Thus, the equation for park attendance is:

$A(t) = 2 \times (1.03)^t$

2. Food Supply

The food supply increases at a constant rate, meaning it's an example of linear growth. The equation for the food supply $F(t)$ after $t$ years is:

$F(t) = F_0 + rt$

where:

• $F_0 = 4$ million people (initial food supply),
• $r = 0.2$ million people per year (annual increase in food supply),
• $t$ is the number of years.

Thus, the equation for the food supply is:

$F(t) = 4 + 0.2t$

Summary:

• Park Attendance: $A(t) = 2 \times (1.03)^t$
• Food Supply: $F(t) = 4 + 0.2t$

Would you like further details or have any questions?

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Here are some related questions:

1. What is the park attendance after 5 years?
2. How much food supply is available after 10 years?
3. After how many years will the park attendance exceed the food supply?
4. What happens to the difference between park attendance and food supply over time?
5. How would the equations change if the food supply increased by 0.5 million people per year instead?
6. What is the percentage increase in park attendance after 10 years?
7. How would the attendance equation change if the growth rate were 5% instead of 3%?
8. What other factors could affect the validity of these equations in real-life scenarios?

Tip: When dealing with exponential growth, always check the base of the exponent to understand the growth rate.