Question

The population of endangered species was estimated to be 240 and 2018 the population has been tracked each year and have been modeled with the geometric sequence 24360 540 8:10 create a function model of the situation

Answer 1

To create a function model for the population of the endangered species based on the information provided, we'll start with the details we've got:

1. The initial population in 2018 was 240.
2. The population grows based on a geometric sequence.

However, your reference to a geometric sequence (24360, 540, 8:10) seems to be unclear. Let's clarify a few things:

A geometric sequence follows a pattern where each term after the first is found by multiplying the previous term by a constant called the common ratio.

Here's how to set up the function given the initial population:

### Step 1: Identify the initial conditions

Let:
- \( P_0 = 240 \) (the initial population in 2018, which we can consider as \( P(0) \))
- Let \( r \) be the common ratio of growth (which would need to be determined).

### Step 2: General form of the geometric sequence

The general form of a geometric sequence can be represented as:

\[
P(n) = P_0 \times r^n
\]

where:
- \( P(n) \) is the population at year \( n \),
- \( P_0 \) is the initial population (240 in this case),
- \( r \) is the growth factor,
- \( n \) is the number of years since 2018.

### Step 3: Determine the common ratio \( r \)

If the population continues to grow, you need at least one more data point to determine the growth factor \( r \). For example, if you had the population in 2019 or any other future year, you could calculate \( r \) using the formula:

\[
r = \frac{P(n)}{P(n-1)}
\]

### Example Function Model

If you find out that the population doubles every 3 years, then:

- If you measure population after, say, 3 years and it's 480, then you would calculate:

\[
r = \frac{480}{240} = 2
\]

The model would look like:

\[
P(n) = 240 \times 2^n
\]

Here, \( n \) is the number of years since 2018.

### Final Model Form

Without additional data points for \( r \), we can't further refine the model. If you do have that input, please provide it, and I can help you create the exact function model!