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The problem provides a population of animals starting at 2,000 in 1998. It mentions that the population increases by 3% each year from 1998 to 2010. The goal is to find the equation that defines the population \( p(x) \), where \( x \) is the number of years after 1998.

The basic structure of an exponential growth model is:
\[
p(x) = p_0 (1 + r)^x
\]
Where:
- \( p_0 \) is the initial population (2000 animals),
- \( r \) is the rate of growth (3% or 0.03),
- \( x \) is the number of years after 1998.

Thus, the equation becomes:
\[
p(x) = 2000(1 + 0.03)^x = 2000(1.03)^x
\]

Looking at the options, the correct one is **C**: 
\[
p(x) = 2000(1.03)^x
\]

Would you like further explanation on exponential growth? Here are 5 questions that build on this concept:

1. What happens if the population decreases by 3% each year instead of increasing?
2. How would the equation change if the population started at a different number, say 5,000?
3. What if the growth rate was 5% instead of 3%? How would the equation look?
4. How can you calculate the population after a specific number of years, like 5 or 10 years?
5. What is the difference between exponential growth and linear growth?

**Tip:** Exponential growth models are used in many real-world applications such as finance, population studies, and radioactive decay.

A function p estimates that there were 2,000 animals in a population in 1998. Each year from 1998 to 2010, the function estimates that the number of animals in this population increased by 3% of the number of animals in the population the previous year. Which equation defines this function, where p(x) is the estimated number of animals in the population x years after 1998?

Solve an exponential growth problem where a population of 2,000 animals in 1998 increases by 3% annually. Learn to define the function p(x) and apply exponential growth formulas. Suitable for high school students, Grades 9-12.

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