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 14 minutes at that elevation, the diver ascended to an elevation of −18
9
10
feet. The total time for the dive so far was 21
1
8
minutes. What was the rate of change in the diver's elevation during the ascent? Round your answer to the nearest hundredth.
To find the rate of change in the diver's elevation during the ascent, we need to first find the change in elevation and then divide it by the time taken for the ascent.
First, let's find the change in elevation. The diver initially descended to an elevation of −89.9 feet and then ascended to an elevation of −18.9 feet. The change in elevation is given by:
Change in elevation = Final elevation - Initial elevation
Change in elevation = -18.9 - (-89.9)
Change in elevation = -18.9 + 89.9
Change in elevation = 71
Next, we need to find the time taken for the ascent. The total time for the dive so far was 21 1/8 minutes, and the diver spent 14 minutes at the first elevation. Therefore, the time taken for the ascent is given by:
Time taken for ascent = Total time - Time spent at initial elevation
Time taken for ascent = 21 1/8 - 14
Time taken for ascent = 21.125 - 14
Time taken for ascent = 7.125
Finally, to find the rate of change in the diver's elevation during the ascent, we divide the change in elevation by the time taken for the ascent:
Rate of change = Change in elevation / Time taken for ascent
Rate of change = 71 / 7.125
Rate of change ≈ 9.93 (rounded to the nearest hundredth)
Therefore, the rate of change in the diver's elevation during the ascent is approximately 9.93 feet per minute.