When modeling the height of a skydiver after jumping from an airplane, we can use the following physics-based equation for free fall under the influence of gravity.
The height \( h(t) \) of the skydiver at time \( t \) seconds after jumping can be modeled by the equation:
\[ h(t) = h_0 - \frac{1}{2} g t^2 \]
where:
- \( h_0 \) is the initial height (10,000 feet),
- \( g \) is the acceleration due to gravity (approximately 32 feet/s² on Earth),
- \( t \) is the time in seconds.
Substituting the values into the equation:
- The initial height \( h_0 = 10,000 \) feet.
- The acceleration due to gravity \( g = 32 \) feet/s².
- We'll calculate for \( t = 7 \) seconds.
Plugging in these values, we calculate:
\[ h(7) = 10,000 - \frac{1}{2} \times 32 \times 7^2 \]
Calculating \( 7^2 \):
\[ 7^2 = 49 \]
Now calculating \( \frac{1}{2} \times 32 \times 49 \):
\[ \frac{1}{2} \times 32 = 16 \]
Then:
\[ 16 \times 49 = 784 \]
Now substituting that back into the height equation:
\[ h(7) = 10,000 - 784 = 9,216 \]
To summarize, the height of the skydiver 7 seconds after they jump out of the airplane is:
\[ \boxed{9,216 \text{ feet}} \]
Based on the provided options, "9,126 feet" would be the closest, but our calculation yields a slightly higher value. Therefore, none of the responses directly match our calculation.