1. You have been hired as a consultant by the company "Bird Baths R Us” to help determine why one of their products is frequently returned by customers.The CEO expects you to justify your conclusions using both graphical and numerical data. You should aim to be as precise as possible in your analysis.Please upload screenshots of any graphical material as well as any Excel files (not screenshots) you use. The product in question is a hemispherical bird bath known as the "Avosphere."It is ten inches deep and features six perches for visiting birds. The height x, in inches, of the water as the Avosphere is being filled is modeled by the differential equation: \frac{d x}{d t}=\frac{60\left(1-20 k x+k x^{2}\right)}{20 x-x^{2}} where the time t is measured in hours and k is a constant that measures how quickly water evaporates. If there were no evaporation, k would be zero. Your preliminary tests have determined k to be .02. We will assume the bird bath initially has 1 inch of water. • In the "DFIELD Direction Field" window menu bar, select Options → Delay Time Per Point → 10 Milliseconds Options → Solution Direction → Forward ● In the “DFIELD Equation" window, you can change the values in the"Display Window." Use Min t = Min x = 0. You will need to decide what you want the maximum values to be. (a) Using your evaporation constant, what is the height of the water after 2hours? What would the height be after 2 hours if there were no evaporation? (b) Assuming no evaporation, how long until the bird bath is full of water? (d) Based on your answers above, why do you think customers are dissatisfied with this product? (e) Approximately what value would Bird Baths R Us need to reduce theevaporation constant to so that customers can get the Avosphere at least70% full? (c) With your evaporation constant, what is the maximum depth of water acustomer can achieve in their Avosphere?

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