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.