To find how long it will take for the fish to reach a depth of -37.8 meters, we first need to calculate how far it needs to descend from its starting depth of -10.8 meters to -37.8 meters.
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Calculate the depth change needed: \[ -37.8 - (-10.8) = -37.8 + 10.8 = -27 \text{ meters} \] So, the fish needs to descend 27 meters.
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Since the fish descends 1.5 meters every 2 minutes, we can find out how many 2-minute intervals it takes to descend 27 meters: \[ \text{Number of intervals} = \frac{27 \text{ meters}}{1.5 \text{ meters/interval}} = 18 \text{ intervals} \]
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Now, calculate the total time: \[ \text{Total time} = 18 \text{ intervals} \times 2 \text{ minutes/interval} = 36 \text{ minutes} \]
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters. This means that after swimming for 36 minutes, the fish will be 27 meters deeper than its starting position of -10.8 meters, resulting in a total depth of -37.8 meters.