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.

Step-by-step explanation:

This is a exponential modelling problem.

The population looses 1/18th of it every 2 months.

That in decimal is:

1/18 = 0.0556

in percentage, 5.56% lost every 2 months

So, remaining:

100 - 5.56 = 94.44%

in decimal that is

0.9444 (to 4 decimal)

Now, the equation modeled would be in the form:

Where

C is the initial amount (185,000)

I is the factor that we decrease by (we found to be 0.9444)

n is the months it decreases by that factor (so, n = 2 cuz every 2 months)

Now we substitute and write the exponential model equation:

5050 i think

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for