The annual attendance at the amusement park is initially 2 million people and is
increasing at 3% per year. The park’s annual food supply is initially adequate for 4
million people and is increasing at a constant rate adequate for an additional 0.2 million
people per year.
a. Write the equation that represents the food supply. Write the equation represents
the park attendance.

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.

Explore how to model park attendance and food supply growth over time with detailed equations. Understand exponential and linear growth concepts applied to real-life scenarios. Calculate attendance after 5 years, food supply after 10 years, and more.

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