https://file.aiquickdraw.com/mathbot/file/1729456560193h1h7sq6z.jpg

To solve the problem shown in the image, we need to write the weight of the rocket as a function of time \( w(t) \).

### Given:
- The initial weight of the rocket is 5100 tons.
- The rocket burns at a rate of 4 tons per minute.
- Time \( t \) is measured in minutes since reentry began.

### Approach:
The rocket's weight decreases linearly over time as it burns fuel at a constant rate of 4 tons per minute. Therefore, the weight of the rocket after \( t \) minutes can be written as:

\[
w(t) = \text{initial weight} - (\text{burn rate}) \times t
\]

Substituting the known values:
- Initial weight: 5100 tons
- Burn rate: 4 tons per minute

\[
w(t) = 5100 - 4t
\]

This equation represents the weight of the rocket as a function of time \( t \).

### Final Answer:
\[
w(t) = 5100 - 4t
\]

Would you like more details or have any questions about this solution?

### Related Questions:
1. How would the equation change if the burn rate were 5 tons per minute?
2. How much time will it take for the rocket to burn half its initial weight?
3. What will the rocket's weight be after 30 minutes of reentry?
4. How can you express the time it takes for the rocket to completely burn up?
5. How would you model the rocket's weight if the burn rate was not constant?

### Tip:
Linear equations like this are useful for modeling situations where something changes at a constant rate, like fuel consumption over time.

A rocket burns up at the rate of 4 tons/min after falling out of orbit into the atmosphere. If the rocket weighed 5100 tons before reentry, express its weight w as a function of the time, t, in minutes, of reentry.

Learn how to express the weight of a rocket burning fuel at 4 tons per minute as a function of time. Given an initial weight of 5100 tons, this problem uses linear equations to model weight changes over time. Suitable for students in Grades 9-11.

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