Let's break down the problem step by step to determine which function rule best represents Tom's weight loss situation.
1. Understand the Initial Condition:
- Tom's initial weight is 160 pounds. This will be our starting point for the function.
2. Weight Loss Per Week:
- Tom loses 2 pounds per week. This means his weight decreases by 2 pounds each week.
3. Mathematical Representation:
- Let [tex]\( x \)[/tex] represent the number of weeks.
- Let [tex]\( y \)[/tex] represent Tom's weight after [tex]\( x \)[/tex] weeks.
4. Formulate the Function:
- Initially, when [tex]\( x = 0 \)[/tex], Tom's weight is 160 pounds.
- After [tex]\( x \)[/tex] weeks, Tom's weight decreases by 2 pounds each week, so the weight lost after [tex]\( x \)[/tex] weeks is given by [tex]\( 2x \)[/tex].
5. Combine the Details:
- The function that represents Tom's weight after [tex]\( x \)[/tex] weeks combines the initial weight and the total weight loss: [tex]\( y = 160 - 2x \)[/tex].
6. Verify the Options:
- The correct function must fit the form [tex]\( y = 160 - 2x \)[/tex].
Let's review the provided options:
1. [tex]\( y = -160 - 2x \)[/tex] - This option is incorrect, as it starts Tom's weight at -160 pounds, which is not realistic based on the given information.
2. [tex]\( y = 2x - 160 \)[/tex] - This option is incorrect, as it suggests weight gain rather than weight loss.
3. [tex]\( y = 2x + 160 \)[/tex] - This option is also suggesting weight gain and not applicable to this scenario.
4. [tex]\( y = 160 - 2x \)[/tex] - This is correct, as it matches our derived function reflecting Tom's weight loss situation.
Therefore, the function that correctly represents Tom's weight loss situation is:
[tex]\[ y = 160 - 2x \][/tex]
So, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
