This problem involves Hooke's Law, which states that the force needed to stretch a spring is directly proportional to the distance the spring is stretched, i.e., $F = kx$, where:

• $F$ is the force in pounds,
• $k$ is the spring constant, and
• $x$ is the extension of the spring in inches.

We are given:

• The spring stretches 16 inches with 7 pounds attached.

First, calculate the spring constant $k$: $k = \frac{F}{x} = \frac{7}{16} = 0.4375 \, \text{pounds per inch}.$

Now, to find the force needed to stretch the spring 22 inches, we use the same formula: $F = kx = 0.4375 \times 22 = 9.625 \, \text{pounds}.$

Therefore, it will take 9.625 pounds to stretch the spring 22 inches. However, none of the choices provided in the image match this exactly. Based on the given answers, this seems like it could be a mistake or a typo in the options.

Would you like further details on this problem?

Here are five related questions for practice:

1. What is Hooke's Law and how is it used in spring problems?
2. How would the force change if the spring constant $k$ doubled?
3. If 10 pounds of force stretched the spring to 20 inches, what would the new spring constant be?
4. How much force would be required to stretch the spring to 30 inches with the same spring constant?
5. How would the formula change if the spring were compressed rather than stretched?

Tip: Always double-check your calculations and the given answer options for potential discrepancies or rounding issues!