Question

The fox population in a certain region has a relative growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 7,900 foxes. a) Find a function that models the population t years after 2000 (t = 0 for 2000). P(t) = b) Use the function from part (a) to estimate the fox population in the year 2015. Round to the nearest fox.

Answer 1

The growth of the fox population can be modeled using the exponential growth formula P(t) = 7900 * e^(0.09t), where t is the years after 2000. To find the population in 2015, we plug in 15 for t in the formula.

Step-by-step explanation:

The subject at hand is exponential growth, a mathematical concept commonly used in population studies. Given that the relative growth rate of the fox population is 9 percent per year, we can write our function to model population over time as P(t) = P0 * e^(rt), where P0 is the initial population, r is the rate of growth, and t is time.

The year 2000 is considered as time zero (t = 0), and the initial population (P0) is 7900 foxes. So when t=0, P(t)=7900. Substituting these values into the formula gives P(t) = 7900 * e^(0.09t).

To estimate the fox population in the year 2015, we substitute 15 (for the 15 years after the year 2000) as the value of t into the function, so P(15) = 7900 * e^(0.09*15). Solving this gives us the approximate population for the year 2015.

Learn more about Exponential Growth