To determine the distance a sloth travels per minute, we can look at the data points provided for the speed of the sloth on the graph.
The points given are:
- (0, 0)
- (0.5, 3)
- (1, 6)
- (1.5, 9)
We can calculate the average speed (distance per minute) between each set of points:
-
From (0, 0) to (0.5, 3): \[ \text{Distance} = 3 \text{ ft} - 0 \text{ ft} = 3 \text{ ft} \] \[ \text{Time} = 0.5 \text{ min} - 0 \text{ min} = 0.5 \text{ min} \] \[ \text{Speed} = \frac{3 \text{ ft}}{0.5 \text{ min}} = 6 \text{ ft/min} \]
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From (0.5, 3) to (1, 6): \[ \text{Distance} = 6 \text{ ft} - 3 \text{ ft} = 3 \text{ ft} \] \[ \text{Time} = 1 \text{ min} - 0.5 \text{ min} = 0.5 \text{ min} \] \[ \text{Speed} = \frac{3 \text{ ft}}{0.5 \text{ min}} = 6 \text{ ft/min} \]
-
From (1, 6) to (1.5, 9): \[ \text{Distance} = 9 \text{ ft} - 6 \text{ ft} = 3 \text{ ft} \] \[ \text{Time} = 1.5 \text{ min} - 1 \text{ min} = 0.5 \text{ min} \] \[ \text{Speed} = \frac{3 \text{ ft}}{0.5 \text{ min}} = 6 \text{ ft/min} \]
In all intervals, the speed is consistently 6 feet per minute.
Therefore, the distance a sloth travels per minute is \( \boxed{6} \) ft. per minute.