To determine the rate of change in the balloon’s altitude, we first find the total change in altitude and then divide that by the time taken to make that change.
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Calculate the change in altitude: \[ \text{Change in altitude} = \text{Final altitude} - \text{Initial altitude} = 200 \text{ feet} - 50 \text{ feet} = 150 \text{ feet} \]
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Calculate the time taken: \[ \text{Time taken} = 7 \text{ minutes} \]
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Calculate the rate of change: \[ \text{Rate of change} = \frac{\text{Change in altitude}}{\text{Time taken}} = \frac{150 \text{ feet}}{7 \text{ minutes}} \approx 21.43 \text{ feet per minute} \]
Thus, the rate of change in the balloon's altitude is approximately 21.43 feet per minute.
This can also be represented as a rational number because \( 150/7 \) is a fraction, which is a form of a rational number.
Correct Response: 21.43 feet per minute