The fox population in a certain region has an annual growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 26000.
(a) Find a function that models the population
t years after 2000 (t= 0 for 2000).
Your answer is p(t)=

To model the population of foxes over time, we can use an exponential growth formula:

\[
P(t) = P_0 \cdot (1 + r)^t
\]

Where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population (in the year 2000),
- \( r \) is the annual growth rate,
- \( t \) is the time in years after the year 2000.

Given:
- \( P_0 = 26000 \),
- \( r = 6\% = 0.06 \).

Thus, the population function becomes:

\[
P(t) = 26000 \cdot (1 + 0.06)^t = 26000 \cdot (1.06)^t
\]

So the function that models the population \( t \) years after 2000 is:

\[
P(t) = 26000 \cdot (1.06)^t
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. What will the fox population be in the year 2010?
2. How long will it take for the fox population to double?
3. What is the population growth over the first 5 years?
4. How does this model change if the growth rate decreases to 4%?
5. What assumptions does this exponential model rely on?

**Tip:** Exponential growth models assume unlimited resources, which may not always be realistic in ecological scenarios!

The fox population in a certain region has an annual growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 26000. (a) Find a function that models the population t years after 2000 (t= 0 for 2000).

Discover how to model the fox population in a region with a 6% annual growth rate. This problem explains the exponential growth formula P(t) = 26000 * (1.06)^t, where t is the number of years after 2000, providing a step-by-step breakdown suitable for Grades 10-12 students.

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