MAT 124 FUNDAMENTALS OF PRECALCULUS I EXTRA-CREDIT ASSIGNMENT. Due date: 05/09

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1 MAT 124 FUNDAMENTALS OF PRECALCULUS I EXTRA-CREDIT ASSIGNMENT Due date: 05/09 Show all your work on the following 10 problems to receive extra credit. Present your work neatly on separate sheets of paper. You may ask for a blue book in the Departmental Office S-220. Use graph paper as needed. You may print graph paper from the course webpage (www2.sunysuffolk.edu/pestiej) and draw graphs by hand, or print out any graphs obtained from an online calculator (such as The grade on this assignment will replace 50% of your lowest exam grade (not including the final exam or the exam that will be dropped). 1

2 The following problems are part of a NSF (National Science Foundation) grant to integrate the topics of green energy into STEM related courses. The focus is to increase awareness of green energy alternatives and increase the number of individuals in the green energy pipeline. Review of Algebra 1) A residential home has approximately forty- 60 watt incandescent light bulbs that are used for an average 2 hours a day. If the average cost is 8.57 cents a kilowatt -hour (1 kwh = Electrical power consumed if 1000 watts of power are used in 1 hour) on Long Island. a) How much does it cost per month to operate the 60 watt lights for a month (assume 30 days)? b) How much does it cost to operate the lights for a year? c) An LED (Light Emitting Diode) light bulb only uses 7 watts of power to create the same amount of light for a 60 watt incandescent light bulb. Calculate the yearly savings in replacing all 60 watt incandescent light bulbs with LED lights. d) Using the results in part c) what would be the total savings for 1.2 million homes in Suffolk County? 2) If two electrical resistors with resistances R1 and R 2 are connected in parallel (see Figure 1), then the total 1 resistance R is given by R (See Figure 1) 1 1 R R 1 2 a) Simplify the expression for R. b) If R1 10 ohms and R2 20 ohms, what is the total resistance R? Figure 1 2

3 Linear Functions 3) Residential electricity rates on Long Island are billed at a monthly charge of $10.12 plus 8.57 cents per kilowatt-hour (1kWh = Electrical power consumed if 1000 watts of power are used in 1 hour) for up to 1000 kilowatt-hours used. a) Write an equation relating the monthly charge C to the number of kilowatt-hours used. b) An average clothes dryer for a family of four uses 200 kilowatt-hours in a month. What is its cost per month? Its cost per year? c) Graph the equation in a) and interpret the slope of the line for the equation in part a. 4) The earth s average surface temperature may be calculated by the function T.02t 15.0, where T is the temperature in ⁰C (Celsius), t is years since Previously to 1950 the average surface temperature was approximately 15 ⁰C. a) What do the slope and T intercept represent? b) Use the equation to predict the average global surface temperature in c) Some predictions state that a 3 o C surface temperature change would cause the oceans to rise above two feet. Using this function determine when the temperature would raise 3 o C temperature. above the 15 o C d) Convert the o C Celsius temperature in part c) to F (Fahrenheit) using the conversion function o 9 F C start Quadratic Functions 5) The power (P) measured in watts produced by a 120 Volt AC (Alternating Current- residential electricity) system having a resistance of 16 ohms is given by P (I) = -16 I I. In this function I denotes current (measured in amps). a) What current is required to produce maximum power? b) Find the maximum power (P) that this system will produce. 3

4 6) A steel drum in the shape of a right circular cylinder is required to have a volume of 100 cubic feet. a) Express the amount A of material required to make the drum, including the top and bottom, as a function of the radius r of the cylinder. b) How much material is required if the drum s radius is 3 feet? c) How much material is required if the drum s radius is 4 feet? d) Graph A=A(r). For what value of r is A smallest? 7) A rain gutter is formed by bending up the sides of a 30-inch-wide rectangular metal sheet as shown in the figure. a) Find a function that models the cross-sectional area of the gutter in terms of x. b) Find the value of x that maximizes the cross-sectional area of the gutter. c) What is the maximum cross-sectional area of the gutter? d) Why is the maximum cross- sectional area important? Functions and Graphs 8) The local electric company calculates bills for its residential customers based on these charges: $10.00 for monthly taxes and adjustments $ per kwh (Kilowatt-hour) charge for the first 300 kwh $ per kwh charge for every kwh above 300 kwh a) Calculate a piecewise defined function for the cost Cx, ( ) where x equals the number of kwh. b) Calculate the monthly electric bill for a family that uses 300kWh. c) Calculate the monthly electric bill for a family that uses 600kWh. 4

5 9) The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is given by t 0 v1.79 ( v v)(33 t) W v (33 t) v 20 where v represents the wind speed (in meters per second) and t represents the air temperature ( o C). Compute the wind chill for: a) An air temperature t 10 o Cand a wind speed v = 1 meter per second. b) An air temperature t 10 o Cand a wind speed v = 15 meters per second. c) An air temperature t 10 o Cand a wind speed v = 25 meters per second. Rational Functions 10) The Doppler Effect is the change in the pitch (frequency) of a sound from a source s as heard by an observer o when the source or the observer are in motion. If the source and the observer are moving in the same direction, the relationship is described by the equation: æ v - v f ' = f o ö a è ç v - v s ø where : f ' = perceived pitch by the observer f a = actual pitch of the source v = speed of sound in air v o = speed of observer v s = speed of the source Suppose you are traveling at 45 mph and you hear an ambulance coming towards you from the rear. The pitch of the siren is 600 hertz (Hz). a) Write a function '(v ) s f that describes this scenario. b) If f ' = 620 Hz, find the speed of the ambulance. c) Graph the function found in part a) above. 5