1 When snowfall was 6 inches the amount of wheat yield was 31 bushels per acre 6 31 When it was 7 5 inches the amount of wheat yield was 36 bushels per acre 7 5 36 a The slope of the line through the 2 points 2 decimal places b The equation of the line slope intercept form c Using your part B answer predict the wheat yield if snowfall was 5 inches 1 decimal place 2 Find the values of x that make the equation true a x 2 4x 28 x 3 The number of boats in the boatyard from 1945 to 1995 can be modeled by this function f x 1 381x 2 83 2x 5865 a Number of years after 1945 where the number of boats reached its maximum capacity Vertex formula b What was the maximum number of boats using your answer from part a Nearest whole number 4 P t 26 3e 0158t is a model that represent the disability rates of those 65 years or older T 0 represents the year 1982 a Estimate the disability rate in 1982 b In 2012 5 U S population that uses the internet from 2000 to 2008 can be modeled by the following function U t 47 73 12 785 ln t t 5 correspond to the year 2000 a What would be the percentage that uses the internet in 2014 6 A shirt company will make a new shirt type Fixed cost of production is 24 050 and variable cost will is 34 per shirt a Total cost function b Marginal Cost c Total cost of making 40 shirts d The number of shirts to have a total cost of 26 124 7 The total cost of a surge protector is C x 6x 1135 The revenue from sales is R x 11x a Profit function b Production level at which the manufacturer will break even c Should the manufacturer sell only 200 d The average cost function 8 A father decides to place 4000 into an investment with an interest rate of 6 for 5 years a The interest is compounded monthly b The interest is compounded continuously 9 Find the equilibrium price and quantity of the following functions a Supply p 1 3q 2 12 b Demand 66 11q 2q 2 formula y t y0e kt 10 The radioactive material vanadium 49 has a half life of 330 days Use this a If 250mg is present find the decay constant k 3 decimal places b Based on your answer write the exponential decay function for all c How much of the 250mg material is left after 800 days 1 decimal values of t place d Rate of change after 800 days 1 decimal place 11 Find the following limit a Lim x 2 8x 15 x 5 x 5 12 an object is thrown upward at 128ft s from a height of 76ft its height after t seconds is given by S t 16t 2 128t 76 a What is the average velocity avg rate of change from t 2 to t 4 The answer can be negative b What is the Instantaneous velocity Instant rate of change at t 2 13 Use the 4 step process to find the derivative of f x 5x 2 2x 3 14 Total cost function C q 95q 2 1080q 3200 Demand function p q 1200 05q a Revenue function b Profit function c Marginal Profit at q 5 15 Use the product rule to find f x f x 5x 2 7x 2 6x 2 3x 16 Suppose a companies total cost function is C x 05x 2 25x 1700 a Average cost function b Marginal average cost function Simplify the numerator in the final answer 17 The percentage of women in the work force from the years 1970 2006 can be modeled by the following function y 47 43 27 93 ln x x represents the number of years after 1950 a What is the percentage of poverty threshold for people in 1980 2 decimal places b 1985 2 decimal places 18 Demand Function p 400 3q 7 1 2 a Rate of Change b Rate of Change at q 3 19 A t 0000284t 3 00505t 2 0613t 4 17 hint quadratic equation 20 Find if the x value of all points where the function G x x 3 3x 2 9x 5 a Increasing b Decreasing a Relative Min b Relative Max 2000 21 The amount of bacteria at a certain time is represented by t 3 t 18 105t a At what time before 7 hours will the population be maximized b What is the maximum population 22 Find f x f x 4x 2 3x 100000 a Find f 0 b Find f 20 23 Find the inflection point from the following function f x 3x 3 9x 2 165x 2 24 Find the point of diminishing returns from the function R x 1 x 3 45x 2 800x hint you should get two points 25 M x 015x 2 1 47x 7 2 30 x 60 a Find the absolute max of the equation b Find the absolute min of the equation 26 A fence must be built to enclose a rectangular area of 45 000 ft 2 Fencing material costs 1 per foot for the two sides north and south and 2 for the other two sides Find the least expensive side 27 A manufacturer sells x phones per week The demand and cost equations per week are listed P 400 5x C x 15 000 130x a What price should the company charge and how many phones should be produced to maximize weekly revenue What is the maximum weekly revenue b What price should the company charge for the phones and how many phones should be produced to maximize the weekly profit What is the maximum weekly profit