Question

Alyssa is an ecologist who studies the change in the fox population of the Arctic circle over time. She observed that the population loses \dfrac{1}{18} 18 1 ​ start fraction, 1, divided by, 18, end fraction of its size every 222 months. The population of foxes can be modeled by a function, PPP, which depends on the amount of time, ttt (in months). When Alyssa began the study, she observed that there were 185{,}000185,000185, comma, 000 foxes in the Arctic circle. Write a function that models the population of the foxes ttt months since the beginning of Alyssa's study.

Answer 1

To model the population of foxes t months since the beginning of Alyssa's study, we can use the equation P(t) = P(0) - (1/18t), where P(0) is the initial population of 185,000 foxes.

Step-by-step explanation:

To write a function that models the population of foxes t months since the beginning of Alyssa's study, we need to determine the rate at which the population decreases over time. Given that the population loses 1/18 of its size every 22 months, we can use this information to develop an equation. Let P(t) represent the population of foxes at time t, and let P(0) be the initial population of 185,000 foxes.

Since the population loses 1/18 of its size every 22 months, the rate of decrease can be calculated as 1/18 per 22 months. This can be written as -1/18 per month or -1/18t per month. Hence, the equation that models the population is P(t) = P(0) - (1/18t).