Question

1. Jin fills up a 510-gallon pool in the backyard for her children. She fills it with the garden hose at a rate of 17 gallons per minute. After it is filled, she lets it sit for 30 minutes in order to let the water temperature rise. The children then get in and have fun for an hour. The pool loses about _1_ gallon of water each minute due to Time (minutes) Amount of Water (gallons) 0 5 20 30 45 60 80 100 120 150 200 2 their splashing and playing. At the end of the hour, they tear the pool while getting out, which causes a leak. The pool then begins to lose water at a rate of 2 gallons per minute. a. Complete the table to show the amount of water in the pool after each minute. b. Create a graph to model the problem situation. Include when the pool will be empty. c. Write a piecewise function that models this problem situation. Explain your reasoning for each piece of the function. d. Identify the x- and y-intercept. Explain what they mean in terms of the problem situation. e. Determine when the pool will have 470 gallons of water in it. Identify the piece(s) of function you used. Explain your reasoning. 2. Jin asks her children to pay her back for the damaged pool. They must give her $15 per week. Together they have $165 in a savings account. a. Write a function to represent the amount of money they have after x weeks. Describe the domain and range of this function in terms of the problem situation. b. To rebuild their account, the children will receive a combined $15 per week in allowances. They start saving the week after their account is depleted and save for another 11 weeks. What are the domain and range of this function and what do they mean in terms of the problem situation? Write a function to represent this part of the graph. c. Graph the equations on the same grid. Is the graph continuous or discrete? Explain your reasoning. d. Write a function to represent the entire graph.

Answer 1

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