A scuba diver dove from the surface of the ocean to an elevation of −89
9
10
feet at a rate of −24 feet per minute. After spending 11.75 minutes at that elevation, the diver ascended to an elevation of −8
9
10
feet. The total time for the dive so far was 18
1
8
minutes. What was the rate of change in the diver's elevation during the ascent? Round your answer to the nearest hundredth.
22.5
nope
To find the rate of change in the diver's elevation during the ascent, we need to calculate the difference in elevation and divide it by the time taken.
The initial elevation was -89
9
10
feet, and the final elevation was -8
9
10
feet.
The difference in elevation = (-8
9
10
) - (-89
9
10
) = 81 feet.
The total time taken was 18
1
8
minutes, and the time spent at the lower elevation was 11.75 minutes.
So, the time taken during the ascent = 18
1
8
- 11.75 = 6.33 minutes.
Now, we divide the difference in elevation by the time taken during the ascent:
Rate of change = difference in elevation / time taken during ascent
Rate of change = 81 feet / 6.33 minutes
Now, let's calculate the rate of change:
Rate of change = 81 / 6.33 ≈ 12.8
Therefore, the rate of change in the diver's elevation during the ascent is approximately 12.8 feet per minute.