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- Suppose the function h gives the cost of Car B t years since 2005. What does the expression 3h(7) represent? 3 times the cost of Car B in 2005 3 times the cost of Car B in 2012 3 dollars more than the cost of Car B in 2012 7 times the cost of 3 Car B's in 2005 7 times the cost of Car B in year 200810. Jingle Bells Inc. has received a rush order for as many of two types of Easter eggs as can be purchased and shipped during a 2-week period. Preliminary analysis by Jingle Bells indicates that the profit on this order isrelated to the number of each type of Easter egg manufactured by the function:P(x1 , x2) = – x12– x22 + 12x1 + 10x2 + 61where x1 = thousands of units of Type 1 eggs and x2 = thousands of units of Type 2 eggs. Because of other commitments over the two weeks, Jingle Bells has available only 60 hours in the Shipping and Packaging Department to get the order out the door. It is estimated that every 1000 units of Type 1 eggs will require 20 hours in the department and every 1000 units of Type 2 eggs will require 30 hours.i) Formulate a mathematical model that can be used to determine how many thousands of each Type of egg should be manufactured in the two-week period so as to maximise profit.ii) Find a solution to your mathematical model.Differentiate the function eln4x + eln4y = 1 implicitly.
- The function w(x) = -0.01x² + 0.27x + 8.60 can be used to estimate the number of self-employed workers in America in millions, x years after 1980. For what years were there (or will be there) 9.7 million self-employed worker in America? (There are 2 answers – a total of 4 points) Answers _________________ and _______________________n 1980, the minimum wage was $3.10 per hour, and in 1997 it was $5.15 per hour. Find a linear function f(x)=mx + b that models the data.A theater finds that there is a correlation between the number of ice cream flavors offered at its food stand and the number of tickets they sell for a show, which can be modeled by the function S(n) =-4n^2 + 192n + 5 where n is the number of ice cream flavors and S(n) is the number of tickets sold. What number of ice cream flavors should be available in order to maximize the number of tickets sold?
- 1) The number S of fuel stations that sold comp natural gas in the united state from 2009 to 2015can be approximated by the functionS ( t ) =69t + 151 9< t < 11= 160t-803 12<t <152) The percent p of prescriptions filled with generic drugs at CVS pharmacies from 2008 through 2014 can be approximated by the model p (t) =2.77t +45.2 8< t < 11p (t) =1.95t + 55.9 12< t< 14Use the model to find the percent of prescriptions filled with generic drugs in each year from2008 through 2014Suppose that "x" years after its founding in 1974, a certain national consumers association had a membership fee of f(x) = 100 (2x^3 - 45x^2 + 264x). At what time between 1975 and 1990 was the membership of the association smallest?Differentiate the function. A (s) =-12/ s 5
- if a linear function for which f(3)=4 and f(-3)=10 find f(7)A major corporation is building a 4,325 acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Clove's population (in thousands) t years from now will be given by the following function. P(t) = (45t^2+125t+200)/(t^2+6t+40) (a) What is the current population (in number of people) of Glen Cove? (b) What will be the population (in number of people) in the long run?Suppose that the number of a certain type of computer that can be sold when its price is P (in dollars) is given by a linear function N(P). Determine N(P) if N(1000) = 10,000 and N(1500) = 7,500. What is the change ∆N in the number of computers sold if the price is increased by ∆P = 100 dollars?