...Part 1. Report to Danny Wilco To: Danny Wilco From: Kay Smith Subject: Re: Ordering product for EBBD from the Kentucky Hooch and Beer Company Background: Our efforts to increase sales of Kentucky Swamp Brew, for our college aged customers, Brew received mixed support from area retailers. For example, our advertising campaign was initially productive, we received a 75% increase in retail orders for three continuous weeks (the duration of the advertising campaign). However, retail orders dropped off 20% when the advertising campaign ended. We appeared to have limited insight on customer interest in Kentucky Swamp Brew and we also failed to properly coordinate with the brewery so they can have supplies on hand to meet projected and actual retail orders. Strategy: For product ordering, I employed a three phase strategy. The first phase was to order more products from KHBC Brewery then current retail order level so we would have inventory on hand to support increased orders, when the advertising efforts took effect. The second phase was to order products based on increased retail order level while adjusting the final order to compensate for brewery delivery in efficiencies. The third phase, towards the end of the Kentucky Swamp Brew sales campaign was to adjust ordering so excess inventory would be controlled. Results: From the attached excel product you will see that our ordering strategy was effective as we were able to stay up with customer demands, compensate...
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...A bullwhip consists of a handle section, a thong, a fall, and a cracker. A wrist loop may also be present, although its chief purpose is for hanging one's whip on a hook. Aesthetically, it finishes the handle. The main portion of the bullwhip's length is made up of a braided body or thong. Made of many strips of leather, the number of braids or plaits is an important factor in the construction of the whip. Often the thong is multi-layered, having one or more "bellies" in the center. Quality whips have at least two bellies, made of braided leather like the surface of the whip, though with fewer plaits. Lower-quality whips may have no bellies at all, and are sometimes stuffed with materials such as newspaper which will break down with use. Unlike in the Australian stock whip, the thong connects in line with the handle (rather than with a joint), or sometimes completely covers the handle. The handle is usually short, being between 8 and 12 inches long. While some whips have an exposed wooden grip, others have an intricately braided leather covered handle. Leather-covered handles usually contain a butt foundation, which is held in the palm of the hand when cracking, and can have a wrist loop, used for hanging the whip at the end of the day, not for putting around the wrist during use. Some handles swivel, making it easier to do certain types of unsophisticated cracks but making it harder to do others, or to use the whip for any type of accurate targeting. The Australians introduced...
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...Flowers in the Attic Wendy Lupton ENG 225 Introduction to Film Jonathan Beller March 25, 2012 Flowers in the Attic Introduction The movie in this essay will be on the 1987 movie the Flowers in the Attic by Jeffrey Bloom. It is a movie where you will feel very suspenseful with all the drama that is happening to the children and what their mother does to stop it. Their grandmother treat’s them very awful when their mother is not home. Storytelling The story of the Flowers in the Attic is four children that fight to survive when slowly forgotten about by their mother played by Victoria Tennant. The mother of four children, who loses her husband and father of the kids, returns to her mother’s mysterious family mansion hoping to regain the love from her father to receive an inheritance. But when the children are imprisoned and abandoned by their evil grandmother, the children must find a way to survive a nightmare of brutal cruelty, forbidden passion and final shocking discovery that will shatter their innocence forever. The children consist of Chris, Cathy, and the two younger children, Cory and Carrie. Little do the children know, their mother has essentially given them over to their abusive, religiously-fanatical grandmother (played by Oscar winner Louise Fletcher), and they are locked away in the attic and kept there, while their health deteriorates and they are abused constantly. All the while, their evil mother conspires to receive the inheritance from her...
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...MAT220 119. Explain how to solve an exponential equation when both sides can be written as a power of the same base. When an exponential equation has both sides of the equation as the same base one needs to rewrite the equation in the form of bM=bN. For instance, 24x-3=8. To make this the same base we need to make 8 a base of two by writing it as 2^3. Then we have 24x-3=23. Then we get rid of the base and get 4x-3=3. Finally we solve for x. 4x-3=3 4x=6 x=23 120. Explain how to solve an exponential equation when both sides cannot be written as a power of the same base. Use 3x = 140 in your explanation. To solve this equation one needs to use a natural logarithm or ln. First take the ln of both sides, ln 3x= ln 140 Then using bx= x ln b, move the variable to the front, x ln 3 = ln 140 Solve for x, x= ln3ln140= 1.0986122887/4.9416424226 = 0.22231723680404. 121. Explain the differences between solving log31x - 12 = 4 and log31x - 12 = log3 4. When solving log31x - 12 = 4 one needs to write it in the form of bc=M. To do this we do the following; logbM=c means bc=M. 1) log31x - 12 = 4 2) 34=x-12 3) 81=x-12 4) x=93 In the case of log31x - 12 = log3 4, since the log is the same on both sides of the equation the will be omitted. The new equation would be; 1x-12=4. Then solve as normal. Add 12 to 4 to get 16, leaving 1x, which is just x and you have x=16. 122. In many states, a 17% risk of a car accident...
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...MA131 0 : Module 2 Exponential a nd Logarithmic Functions Exercise 2 .2 Solving Exponential and Logarithmic Equations 1 Answer the following questions to complete this exercise: 1. Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents: 6 x = 216 2. Solve the following exponential equation: e x = 22.8 Express the solution in terms of natural logarithms. Then, use a calculator to obtain a decimal approximation for the solution. 3. Solve the following logarithmic equation: log 7 x = 2 Reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer. 4. Solve the following logarithmic equation: log ( x + 16) = log x + log 16 Reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer. 5. The population of the world has grown rapidly during the past century. As a result, heavy demands have been made on the world's resources. Exponential functions and equations are often used to model this rapid growth, and logarithms are used to model slower growth. The formula 0.0547 16.6 t Ae models the population of a US state, A , in millions, t years after 2000. a. What was the population in 2000? b. When will the population of the state reach 23.3 million? 6. The goal of our financial security depends on understanding how money in savings accounts grows in remarkable...
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...Nina Hills MAT 205 /Week 2 Focus on Application 07/11/2014 The concept of this week was to look at function problems that can include exponentials and logarithms with functions. These functions help with situations such as profit analysis, compound interest, continues compound interest or even doubling time for an investment. An example that I have that would go very well with today’s day in age would be simply the economy on its own. Our economy has taken such a huge turn downhill due to big banks making poor choices of investment. With that, many people don’t have savings accounts, 401K’s and such for their own future ahead. These two examples are examples of ways we may save for our retirement, but at this point there is a bare chance of that happening at an earlier on age. Many will have to work longer throughout their lives just to make sure that they are financially set when entering retirement. With the concepts of this week, we can calculate how long it would take to double a certain amount of investment in a certain time period with a fixed interest rate that would play upon a certain interval. A=P(1+r/m)^mt This equation can help determine t (time), for the principal to double. We can put in 2P for A, due to the other known values are r (interest rate) and m=1. Once we solve for t, we know the amount of time it will take to double our investment. With this week’s concept, we can predict at a pretty accurate rate the amount of time it takes to grow...
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...model a variety of realworld phenomena: growth of populations of people, animals, and bacteria; radioactive decay; epidemics; absorption of light as it passes through air, water, or glass; magnitudes of sounds and earthquakes. We consider applications in these areas plus many more in the sections very important. As a part of our BBA course, we are required to submit a term paper for every subject each semester. As our Advance Business Mathematics faculty Associate Professor Lt. Col. Md. Showkat Ali has asked us to submit a term paper on a topic upon our will. So, we have decided to choose “Exponential & Logarithmic Functions”. to graph exponential functions to evaluate functions with base e to learn the use of compound interest formulas to learn the changing from logarithmic to exponential form to learn the changing from exponential to logarithmic form to learn the evaluation of logarithms to learn the use of basic logarithmic properties to learn the use of graph logarithmic functions to find the domain of a logarithmic function to learn the use of common logarithms to learn the use of natural logarithms to learn the use of the product rule to learn the use of the quotient rule to learn the use of the power rule to...
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...This lab requires you to: • Evaluate exponential functions. • Graph exponential functions. • Evaluate functions with base e. • Change from logarithmic to exponential form. • Change from exponential to logarithmic form. • Evaluate logarithms. • Use basic logarithmic properties. • Graph logarithmic functions. • Find the domain of a logarithmic function. • Use common logarithms. • Use natural logarithms. • Use the product rule. • Use the quotient rule. • Use the power rule. • Expand logarithmic expressions. • Condense logarithmic expressions. • Use the change-of-base property. Answer the following questions to complete this lab: 1. State in a few words, what is an exponential function? 2. What is the natural exponential function? 3. Evaluate 4–1.5 using a calculator. Round your answer to three decimal places. 4. The formula S = C (1 + r)^t models inflation, where C = the value today r = the annual inflation rate S = the inflated value t years from now Use this formula to solve the following problem: If the inflation rate is 3%, how much will a house now worth $510,000 be worth in 5 years? 5. Write 6 = log2 64 in its equivalent exponential form. 6. Write 8y = 300 in its equivalent logarithmic form. 7. Hurricanes are some of the largest storms on earth. They are very low pressure areas with diameters of over 500 miles. The barometric air pressure in inches of mercury at a distance of x miles from the eye of a severe hurricane is modeled by the formula...
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...This is an essay about nothing in order to qualify for this site it must contain at least 250 words. So On the left-hand side above is the exponential statement "y = bx". On the right-hand side above, "logb(y) = x" is the equivalent logarithmic statement, which is pronounced "log-base-b of y equals x"; The value of the subscripted "b" is "the base of the logarithm", just as b is the base in the exponential expression "bx". And, just as the base b in an exponential is always positive and not equal to 1, so also the base b for a logarithm is always positive and not equal to 1. Whatever is inside the logarithm is called the "argument" of the log. Note that the base in both the exponential equation and the log equation (above) is "b", but that the x and y switch sides when you switch between the two equations.PrintHidden<p><font face="Arial" size="2" color="#000000">Note: The graphic in the box below is animated in the original ("live") web lesson.</font></p> —The Relationship Animated— | | If you can remember this relationship (that whatever had been the argument of the log becomes the "equals" and whatever had been the "equals" becomes the exponent in the exponential, and vice versa), then you shouldn't have too much trouble with logarithms. Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved //(I coined the term "The Relationship" myself. You will not find it in your text, and your teachers and tutors will have no idea...
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...and brought the microscope over to my work area, making sure to carry the microscope by the arm and base. I uncovered and plugged in the microscope. I then went back to the cart and got a slide and slide cover, as well as a small glass bottle and dropper. I filled the small glass bottle with water and took everything back to my work area. I wrote a letter e on a piece of paper with a pen, pulled a strand of hair from my head and pulled a string off of my jacket. Then I turned on the microscope, prepared my slide and proceeded to look at each object under the microscope. Data: If the slide was too close or too far from the lens than you will not be able to see the specimen. The larger the magnification on the microscope the more detail that can be seen. The course and fine adjustment knobs move the slide up and down to help focus the specimen on the slide. The mechanical stage controls move the slide left and right, and forward and backwards. Findings: While observing the hair under the microscope I noticed that it is not smooth. The hair actually looks like it is made up of tiny scales. While observing the paper with the letter e written on it, I noticed that, just like the hair, the paper does not look smooth. The paper actually looks like a bunch of threads woven together like a birds nest. The ink on the paper only seemed to stick to the top layer or two of the paper material. I also observed that the letter appeared upside down and...
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...A Generalized Logarithm for Exponential-Linear Equations Dan Kalman Dan Kalman (kalman@email.cas.american.edu) joined the mathematics faculty at American University in 1993, following an eight year stint in the aerospace industry and earlier teaching positions in Wisconsin and South Dakota. He has won three MAA writing awards, is an Associate Editor of Mathematics Magazine, and served a term as Associate Executive Director of the MAA. His interests include matrix algebra, curriculum development, and interactive computer environments for exploring mathematics, especially using Mathwright software. How do you solve the equation 1.6x = 5054.4 − 122.35x? (1) We will refer to equations of this type, with an exponential expression on one side and a linear one on the other, as exponential-linear equations. Numerical approaches such as Newton’s method or bisection quickly lead to accurate approximate solutions of exponential-linear equations. But in terms of the elementary functions of calculus and college algebra, there is no analytic solution. One approach to remedying this situation is to introduce a special function designed to solve exponential-linear equations. Quadratic equations, by way of analogy, are √ solvable in terms of the special function x, which in turn is simply the inverse of a very special and simple quadratic function. Similarly, exponential equations are solvable in terms of the natural logarithm log, and that too is the inverse of...
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...Question 1 Evaluate the function at the indicated value of x. Round your result to three decimal places. Function: f(x) = 0.5x Value: x = 1.7 | | -0.308 | | | 1.7 | | | 0.308 | | | 0.5 | | | -1.7 | 5 points Question 2 Match the graph with its exponential function. | | y = 2-x - 3 | | | y = -2x + 3 | | | y = 2x + 3 | | | y = 2x - 3 | | | y = -2x - 3 | 5 points Question 3 Select the graph of the function. f(x) = 5x-1 | | | | | | | | | | | | | | | 5 points Question 4 Evaluate the function at the indicated value of x. Round your result to three decimal places. Function: f(x) = 500e0.05x Value: x=17 | | 1169.823 | | | 1369.823 | | | 1569.823 | | | 1269.823 | | | 1469.823 | 5 points Question 5 Use the One-to-One property to solve the equation for x. e3x+5 = 36 | | x = -1/3 | | | x2 = 6 | | | x = -3 | | | x = 1/3 | | | x = 3 | 5 points Question 6 Write the logarithmic equation in exponential form. log8 64 = 2 | | 648 = 2 | | | 82 = 16 | | | 82 = 88 | | | 82 = 64 | | | 864 = 2 | 5 points Question 7 Write the logarithmic equation in exponential form. log7 343 = 3 | | 7343 = 2 | | | 73 = 77 | | | 73 = 343 | | | 73 = 14 | | | 3437 = 2 | 5 points Question 8 Write the exponential equation in logarithmic form. 43 = 64 | | log64 4 = 3 | | | log4...
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...1. An exponential function is a function with a constant base that is changed by x, a variable. Exponential functions are used to predict changes in murder rates, bacteria growth even investments. This function can also be used in predicting rate of decay such as automobile value and radioactive half-life. 2. The natural exponential function, f(x) = ex, has a known base constant. Unlike other exponential functions where the constant, a, can be any real number, e is always 2.718. A good example of a natural exponential function is continuous compound interest. 3. Evaluate 4-1.5 = 0.125 4. Using the formula S = C(1 + r)t If the inflation rate is 3%, how much will a will a house now worth $510,000 be worth in five years? S = $510,000 ( 1 + .03 )5 S = $510,000 x 1.035 S = $591,229.78 5. Write 6 = log2 64 in its equivalent exponential form. y = loga x 6 = log2 64 x = ay 64 = 26 6. Write 8y = 300 in its equivalent logarithmic form. y = bx 300 = 8y logb (y) = x log8 (300) = y 7. Using the formula: f(x) = 0.48 In (x+1) + 27 a. Evaluate f(0) and f(100). Interpret the result. f(0) = 0.48in (1) + 27 = 27 says the barometric pressure at the eye is 27 f(100) = 0.48 (101) + 27 = 29.215 says the barometric pressure 100 miles from the eye is approximately 29.2 b. At what...
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...accurate b. As the percentage increases towards 100% the rate of kids that volunteer will slow and a large number of years will be needed to continue to approach 100% representative of a logarithmic function. An exponential function would reach 100% in a few years, which is not representative of the rate at which the kids are volunteering. 56. H=-[.521log2.521+.324log2.324+.0811log2.0811+.074log2.074] H=1.59 Section 4.5 6. 5x=13 Ln5x=13 Xln5=ln13 X = ln13/ln5 = 1.59 24. 5(1.2)3x-2 + 1 = 7 5(1.2)3x-2=6 ln1.23x-2=ln6/5 (3x-2)ln1.2 = ln6/5 3x-2 = ln(6/5)/ln1.2 3x = [ln(6/5)/ln1.2] +2 X = [[ln(6/5)/ln1.2] +2]/3 X=1 60. R=p-kln(t) r-p=-kln(t) p-r=kln(t) (p-r)/k = ln(t) e[(p-r)/k]=t 76. 20,000=16,000(1+r/4)5.25*4 1.25=(1+r/4)21 Ln1.25 = 21ln(1+r/4) Ln1.25/21 =ln(1+r/4) e.010626=1+r/4 1.0107 = 1+r/4 .0107=r/4 r=.04, therefore rate...
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...1. Read Module 3 Topic 7, Module 4 Topic 1 and 2, Module 5 Topic 1~2. 2. Do the drills for the topics. 3. Read the Chapter 3 sections 2, 5 and Chapter 4 sections 1~3 in your textbook. 4. Do Homework for week 5 (you can find the list in the conference). Week 5 Supplementary Notes Chapter 3 Section 3.2: Polynomial Function of Higher Degree A polynomial function P is given by , where the coefficients are real numbers and the exponents are whole numbers. This polynomial is of nth degree. Far-Left and Far-Right Behavior The behavior of the graph of a polynomial function as x becomes very large or very small is referred to as the end behavior of the graph. The leading term of a polynomial function determines its end behavior. x becomes very large x → ∞ x becomes very large x → ∞ x becomes very small -∞ ← x x becomes very small -∞ ← x We can summarize the end behavior as follows: The Leading-Term Test If is the leading term of a polynomial, then the behavior of the graph as x → ∞ or as x → −∞ can be described in one of the four following ways. If n is even and an >0: ▼ ▼ | If n is even and an <0:▲ ▲ | If n is odd and an >0: ▲▼ | If n is odd and an <0: ▲ ▼ | Polynomial Function, Real Zeros, Graphs, and Factors (x − c) If c is a real zero of a function (that is, f(c)=0), then (c,0) is an x-intercept of the graph...
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