tyler filled up his bathtub, took a bath, and then drained the tub. the function b gives the depth of the water, in inches, t minutes after tyler began to fill the bathtub. explain the meaning of each statement in this situation. a. b(0) = 0 b. b(1) b(40)

Question

tyler filled up his bathtub, took a bath, and then drained the tub. the function b gives the depth of the water, in inches, t minutes after tyler began to fill the bathtub. explain the meaning of each statement in this situation. a. b(0) = 0 b. b(1) < b(7) c. b(9) = 11 d. b(10) = b(22) e. b(20) > b(40)

Accepted Answer

### Part a
# Brief Explanations:
In the function $ B(t) $, $ t $ is the time in minutes after Tyler started filling the tub, and $ B(t) $ is the water depth in inches. When $ t = 0 $, it's the start time. So $ B(0)=0 $ means at 0 minutes (the moment Tyler began filling the tub), the depth of the water in the bathtub was 0 inches (the tub was empty initially).
# Answer:
At the moment Tyler began filling the bathtub (0 minutes after starting), the depth of the water in the bathtub was 0 inches (the tub was empty).

### Part b
# Brief Explanations:
$ B(1) $ is the water depth at 1 minute, and $ B(7) $ is the depth at 7 minutes. The inequality $ B(1)<B(7) $ implies that the depth of the water 1 minute after starting to fill the tub is less than the depth 7 minutes after starting. Since Tyler was filling the tub (before draining), this means the tub was still being filled between 1 and 7 minutes, so the water got deeper over that time.
# Answer:
1 minute after Tyler began filling the bathtub, the depth of the water was less than the depth of the water 7 minutes after he began filling the bathtub. This suggests the tub was still being filled between 1 and 7 minutes, so the water depth increased over that period.

### Part c
# Brief Explanations:
For the function $ B(t) $, when $ t = 9 $, $ B(9) = 11 $ means 9 minutes after Tyler started filling the tub, the depth of the water in the bathtub was 11 inches.
# Answer:
9 minutes after Tyler began filling the bathtub, the depth of the water in the bathtub was 11 inches.

### Part d
# Brief Explanations:
$ B(10) $ is the depth at 10 minutes, and $ B(22) $ is the depth at 22 minutes. The equation $ B(10)=B(22) $ means the depth of the water 10 minutes after starting to fill the tub is equal to the depth 22 minutes after starting. This could happen if between 10 and 22 minutes, Tyler filled the tub to a certain level, maybe took a bath (keeping the depth constant for some time), or drained and then refilled, but in this context, likely that the depth at 10 minutes (maybe during filling or a steady state) is the same as at 22 minutes (maybe during draining or another steady state, but the key is the depths are equal at these two different times).
# Answer:
10 minutes after Tyler began filling the bathtub, the depth of the water in the bathtub was equal to the depth of the water 22 minutes after he began filling the bathtub. This could indicate that the water depth was the same at these two different times (e.g., maybe the tub was being filled, then maybe held at a level, or drained and refilled to the same depth, etc.).

### Part e
# Brief Explanations:
$ B(20) $ is the depth at 20 minutes, and $ B(40) $ is the depth at 40 minutes. The inequality $ B(20)>B(40) $ means the depth of the water 20 minutes after starting to fill the tub is greater than the depth 40 minutes after starting. Since Tyler drained the tub after bathing, this implies that by 40 minutes, the tub had been drained (or was in the process of draining) such that the depth at 40 minutes was less than at 20 minutes.
# Answer:
20 minutes after Tyler began filling the bathtub, the depth of the water in the bathtub was greater than the depth of the water 40 minutes after he began filling the bathtub. This suggests that by 40 minutes, the tub had been drained (or was draining) so that the water depth decreased from 20 minutes to 40 minutes.

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Question

Explanation:

Part a

Answer:

Part b