Question

The population of deer in a national forest has been increasing by about 5.8% annually. The current population is about 2,200 deer. Which function models the total number of deer, after x years?

Answer 1

The function that models the deer population after x years, with a 5.8% annual growth rate, is P(x) = 2,200 × (1 + 0.058)x, where P(x) represents the population after x years.

Step-by-step explanation:

The function that models the total number of deer in the national forest after x years, given an annual increase of 5.8%, can be represented by an exponential growth function. The initial population is 2,200 deer. The formula for exponential growth is P(t) = P0 × (1 + r)t, where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the time in years.

To apply this formula to our scenario with a 5.8% annual increase, we convert the percentage into a decimal to get r = 0.058. Thus, the function for the deer population after x years is P(x) = 2,200 × (1 + 0.058)x.