Questions: The fox population in a certain region has an annual growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 19500. (a) Find a function that models the population t years after 2000 ( t=0 for 2000). Your answer is P(t)=

Solution Steps

The fox population can be modeled using the exponential growth formula:

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

where:

• \( P_0 = 19500 \) (initial population in the year 2000),
• \( r = 0.09 \) (annual growth rate),
• \( t \) is the number of years after 2000.

To find the population in the year 2005, we substitute \( t = 5 \) into the function:

\[ P(5) = 19500 \cdot (1 + 0.09)^5 \]

Calculating \( (1 + 0.09)^5 \):

\[ (1.09)^5 \approx 1.53862 \]

Now, substituting this value back into the equation:

\[ P(5) \approx 19500 \cdot 1.53862 \approx 30003.1671 \]

Rounding \( 30003.1671 \) to four significant digits gives us:

\[ P(5) \approx 30003.17 \]

Final Answer