Your above-ground pool has sprung a leak, and you do not have a way to...
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Your above-ground pool has sprung a leak, and you do not have a way to fix it. At 12 noon, the water in the pool is 5 feet deep (in other words, the water level is 5 feet above the ground). You are not sure how quickly the pool level is falling, so you check again after 40 minutes and see that the height of the water level is now 4 feet. You notice that there is a relationship between the time that has passed to the height of the water level in the pool. (a) If you assume the height of the water level is decreasing at a constant rate, what will be the height of the water level at 1 p.m.? (b) Write a linear function, h, that relates the time past noon, t, in minutes, and the height of the water level in the pool, h(t), in feet. (c) Explain the meaning of the rate of change of function h. (d) Evaluate h(75), and explain its meaning in the context of time passed and height of the water level. (e) At what time, t, will h(t)=0.5? What does your solution mean in the context of the problem? (f) When you check the pool at 3 p.m., the height of the water level is approximately 1 foot, 4 inches. What conclusions can you draw?
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