A scuba diver dove from the surface of the ocean to an elevation of −79
9
10
feet at a rate of −22.8 feet per minute. After spending 14.25 minutes at that elevation, the diver ascended to an elevation of −38
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.
The rate of change of the diver's elevation was
ft/min.
To find the rate of change in the diver's elevation during the ascent, we need to determine the change in elevation and divide it by the time taken for the ascent.
The diver initially descended from the surface to an elevation of -79 9/10 feet. Then, after spending 14.25 minutes at that elevation, the diver ascended to an elevation of -38 9/10 feet.
To find the change in elevation, we subtract the initial elevation from the final elevation:
Change in elevation = final elevation - initial elevation
Change in elevation = (-38 9/10) - (-79 9/10)
Change in elevation = -38 9/10 + 79 9/10
To add or subtract fractions, we need to have a common denominator. In this case, we can rewrite the mixed numbers as improper fractions:
Change in elevation = (-38/10) + (79/10)
Change in elevation = (-38 + 79) / 10
Change in elevation = 41 / 10
Now we can calculate the rate of change using the formula:
Rate of change = change in elevation / time taken for ascent
In this case, the time taken for the ascent is the total time for the dive (21 1/8 minutes) minus the time spent at the first elevation (14.25 minutes):
Time taken for ascent = total time for the dive - time spent at first elevation
Time taken for ascent = (21 1/8) - 14.25
Time taken for ascent = (169/8) - (113/8)
Time taken for ascent = 56/8
Time taken for ascent = 7
Substituting the values into the formula:
Rate of change = (41/10) / 7
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
Rate of change = (41/10) * (1/7)
Rate of change = 41/70
Rounding the answer to the nearest hundredth:
Rate of change = 0.59 ft/min
Therefore, the rate of change in the diver's elevation during the ascent is approximately 0.59 ft/min.