Algebra 2 Enhanced Massey Unit 5 – HW #8 – Modeling Polynomials Name___________________________________________ Period____Date__________________________________ 1.) Squares with side length of 𝑥 are cut from the corners of a rectangular piece of sheet metal with dimensions of 5 in. x 13 in. The metal is the folded to make an open-top box. a. Write a function for the volume. b. Describe the feasible domain for 𝑉(𝑥). c. Find the maximum possible volume of the box. d. Find the dimensions of the maximum volume box. 2.) Carrie Awnbag is going on vacation and she wants to purchase one carry-on bag in which to pack all of her belongings. Most carry-on luggage have a length 10 inches greater than their depth. The airline regulations state the baggage should not exceed 50 linear inches. (sum of the length, width, and depth). a. Write an equation for the volume of the carry-on baggage as a function of the depth, 𝑑. b. Describe the feasible domain for the volume function. c. If she wants to have the maximum volume for her carry-on luggage, what dimensions should she look for when purchasing the luggage? What is the maximum volume? 3.) Use finite differences to find the degree of the polynomial that models the data below. 𝑥 -3 -2 -1 0 1 2 3 4 5 𝑓(𝑥) 115 33 7 1 3 25 103 297 691 4.) A biologist is doing research on the speed of bacterial growth and he decides to track the number of the bacteria as time goes on. He makes a table of values with one variable being time in days and the other variable being the number of the bacteria in thousands. Find a polynomial function that models the speed of bacterial growth. Time (𝑥) 1 2 3 4 5 6 7 Bacteria (𝑦) 17.5 34 76.5 157 287.5 480 746.5 Estimate how many bacteria he can expect after 12 hours. 5.) A gymnast dismounts from the balance beam, the height from the ground, ℎ(in feet) is recorded as various time intervals, 𝑡(in seconds)/ Time 0.15 0.2 0.4 0.5 0.6 0.8 1.0 1.1 Height 7.0 9.1 11.0 11.5 11.1 8.3 5.4 2.1 a. Use the best model to find the maximum height the gymnast is above the ground. b. Use the best model to determine how long the gymnast has to complete the dismount. 6.) When an earthquake occurs, seismic waves are detected thousands of kilometers away from the epicenter within a matter of minutes. The table gives the travel time of a primary seismic wave and the corresponding distance from the epicenter for several minutes. Travel Time 1 2 5 7 10 12 13 (minutes) Dinstance 320 1600 2500 2000 4100 4200 3100 (km) a. Find the quartic regression equation that models the data. Round decimals to three decimal places. b. Using the equation, determine how far away from the epicenter will the wave be felt 8.5 minutes after the quake occurs.