The International Space Station travels in its orbit around Earth at a constant speed of 17,500 miles per hour. The function D(t) represents the total distance that the International Space Station has traveled, t hours since it first entered Earth orbit.
What is the range of D(t)?

The range of the function \( D(t) \), which represents the total distance traveled by the International Space Station (ISS) after \( t \) hours, depends on the values that \( D(t) \) can take.

### Function Description:
Since the ISS is traveling at a constant speed of 17,500 miles per hour, the total distance it travels after \( t \) hours is given by:
\[
D(t) = 17,500 \times t
\]
where \( t \) is the time in hours, and \( D(t) \) is the distance in miles.

### Range of \( D(t) \):
- The minimum value of \( t \) is 0, which represents the time when the ISS first entered Earth's orbit.
- As \( t \) increases, the value of \( D(t) \) also increases without bound.

Thus, the range of \( D(t) \) is all non-negative real numbers, or:
\[
\text{Range of } D(t): [0, \infty)
\]

This means that the ISS can travel any distance from 0 miles to an infinitely large distance, as time increases.

Would you like further details or any clarifications?

### Relative Questions:
1. How would the range change if the ISS speed were variable instead of constant?
2. What is the domain of \( D(t) \)?
3. How long does it take for the ISS to complete one full orbit around Earth?
4. How many miles would the ISS travel in 24 hours?
5. How would you express the function \( D(t) \) if the speed was given in kilometers per hour?

### Tip:
In problems involving constant speed, distance is always a linear function of time, where the slope equals the speed.

The International Space Station travels in its orbit around Earth at a constant speed of 17,500 miles per hour. The function D(t) represents the total distance that the International Space Station has traveled, t hours since it first entered Earth orbit. What is the range of D(t)?

Explore the distance-time relationship for the International Space Station traveling at a constant speed of 17,500 miles per hour. Learn how to determine the range of the function D(t) and understand key linear function concepts. This problem is suitable for students in Grades 6-8 and demonstrates how distance is directly proportional to time.

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