To find the constant of proportionality, we first need to understand how depth underwater relates to time in this scenario.
The diver descended:
- 64 feet in 4 minutes
- 96 feet in 6 minutes
We can determine the rate of descent in feet per minute.
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Calculate the depth per minute for both time intervals:
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From 0 to 4 minutes:
- Depth = 64 feet
- Time = 4 minutes
- Rate = \( \frac{64 \text{ feet}}{4 \text{ minutes}} = 16 \text{ feet per minute} \)
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From 0 to 6 minutes:
- Depth = 96 feet
- Time = 6 minutes
- Rate = \( \frac{96 \text{ feet}}{6 \text{ minutes}} = 16 \text{ feet per minute} \)
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Determine the constant of proportionality:
Since both calculations give us the same rate of descent, the constant of proportionality (the rate at which the diver descends) is 16 feet per minute.
Therefore, the constant of proportionality is 16.