https://file.aiquickdraw.com/mathbot/file/1726628838201xuqzrpjy.jpg

Let's analyze the problem and provide a solution.

### Part (a): Is \( F \) a function of \( t \)?
A function is a relation where each input (in this case, \( t \), representing the month) corresponds to exactly one output (here, \( F \), representing the fox population). From the given dataLet's analyze the problem and provide a solution.

### Part (a): Is \( F \) a function of \( t \)?
A function is a relation where each input (in this case, \( t \), representing the month) corresponds to exactly one output (here, \( F \), representing the fox population). From the given 

\[
\begin{aligned}
t & : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 \\
F & : 150, 143, 125, 100, 75, 57, 50, 57, 75, 100, 125, 143
\end{aligned}
\]

Each value of \( t \) corresponds to exactly one value of \( F \). Therefore, **yes, \( F \) is a function of \( t \)**.

### Part (b): Finding the values of \( t \) where \( g(t) = F(t) = 75 \)
From the table, we are looking for all \( t \) such that \( F(t) = 75 \).

\[
\begin{aligned}
t & : 4, 8 \\
F(t) & : 75
\end{aligned}
\]

So, the values of \( t \) where \( F(t) = 75 \) are **\( t = 4, 8 \)**.

Let me know if you would like more details or have any questions!

### Related Questions:
1. What defines a function in mathematical terms?
2. Can a function have more than one output for a single input?
3. How do we determine solutions to equations from tables of values?
4. What are the characteristics of a one-to-one function?
5. How do you represent functions graphically?

**Tip**: When dealing with tables of values, always check that each input corresponds to only one output to verify if the relation is a function!

A national park records data regarding the total fox population F over a 12 month period, where t = 0 means January 1, t = 1 means February 1, and so on. Is F a function of t? Let g(t) = F denote the fox population in month t. Find all solution(s) to the equation g(t) = 75.

Analyze if F is a function of t based on a 12-month fox population data table. Learn how to find all solutions where the fox population equals 75 in given months. Suitable for students in Grades 8-10.

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