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## MATH 109 Test 3 Review

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**Potpourri 100**• Suppose that a quadratic function has a maximum at its vertex at the point (-5, 22). How many zeros does the quadratic function have? • Answer: 2**Potpourri 200**• Find an equation for a quadratic function that does not cross the x-axis and has a negative vertical intercept • Answers will vary**Potpourri 300**• When rabbits were first brought to Australia, they multiplied very rapidly because there were no predators. In 1865, there were 60,000 rabbits. By 1867, there 2,400,000 rabbits. Assuming exponential growth, when was the first pair of rabbits introduced into the country? • Answer: Around 1859**Potpourri 400**• The consumer price index compares the cost of goods and services over various years. The base year for comparison is 1967. The same goods and services that cost $100 in 1967 cost $184.50 in 1977. Assuming that costs increase exponentially, when did the same goods and services cost double that of 1967? • Answer: 1978**Potpourri 500**• When a murder is committed, the temperature of the body cools according to the equation: • Suppose after two hours, the body cools to 35 degrees C. Find r . • r = -0.7155 • Suppose the police find a dead body with a temperature of 30 degrees C at 4 pm. Use this information to determine when the murder was committed? • Answer: 7:13am**Potent Potables 100**• Plutonium, the fuel for atomic weapons, has a half-life of 24,400 years. Most atomic weapons are designed with a 1% mass margin. This means the weapon will remain functional until the original fuel has decayed more than 1% (leaving 99% of the original amount). Estimate how many years a plutonium bomb would remain functional. • About 354 years**Potent Potables 200**• The proportion of carbon-14, an isotope of carbon, in living plant matter is constant. Once a plant dies, the carbon-14 in it begins to decay with a half-life of 5570 years. An archaeologist measures the remains of carbon-14 in a prehistoric hut and finds it to be one-tenth the amount of carbon-14 in the living wood. How old is the hut? • Answer: 18,503 years old**Potent Potables 300**• Solve for x: • Answer: x = -1**Potent Potables 400**• During a hot summer day, the air conditioning unit in your apartment goes out. The time, t, in hours after your AC went out is given by the equation: • where H is the temperature (in degrees Fahrenheit) of your apartment at that time. • What is the temperature of your apartment when your AC goes out? • About 70 degrees F**Potent Potables 500**• The population of a town was initially 10,000 and grew to 15,000 in 5 years. Assuming exponential growth complete the table given below:**Quads 100**• Find an equation for a quadratic function with vertex (h,k) where h < 0 and k > 0 and has a positive y-intercept. • Answers will vary**Quads 200**• Find the equation of a quadratic function with zeros at 2 and -4 and passing through the point (0,4).**Quads 300**• For the quadratic function graphed below, find (i) an equation (ii) the vertex (iii) focal point**Quads 400**• Rewrite the following quadratic in vertex form: • Find the zeros of this quadratic function. • Vertex: • Zeros: 0.551 and 5.450**Quads 500**• A quadratic function f(x) has vertex at (2,k) where k is a real number, and passes through the point (-1,3). Explain under what conditions this function would have no x-intercepts. Determine the values of k so that f(x) has no x-intercepts • 0<k<3**Quad Applications 100**• A horticulturist has determined that the number of inches a young redwood tree grows in one year is a function of the annual rainfall, r (in inches), given by: • What is the maximum number of inches a young redwood can grow in a year? • 13.5 inches**Quad Applications 200**• A stone thrown downward with an initial velocity of 49 m/s will travel a distance of s meters according to the function • Where t is measure in seconds. • If a stone is thrown downward with an initial velocity of 49 m/s from a height of 274.4 meters, how long until the stone hits the ground? • 4 seconds**Quad Applications 300**• A slim line fluorescent bulb with ½ inch diameter needs 1 inch clearance top and bottom in a parabolic reflecting shade. • What are the coordinates of the focus? • (0, -1.25) • What is the equation for this reflector? • What is the diameter of the opening of the shade? • 7.07 ft**Quad Applications 400**• A bakery sells specialty pies during a six month period. In order to make the most money, the bakery changes the price of the pies to see how sales are affected. • How many pies should they sell and at what price to make the most money? • 475 pies at $9.50 per pie**Quad Applications 500**• A diary farmer has 1500 feet of fencing. He wants to use all 1500 feet to construct a rectangle and two interior separators that together make three rectangular pens. • Determine the dimensions of the larger rectangle that gives the maximum area. • L = 375 ft W = 187.5 ft