"Function" Essays and Research Papers

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  • Logistic Function and Population

    7 Project ll One of the most common models of population growth is the exponential model. These models use functions of the torm p(t) : po€rt‚ wherep6 is the initial population and r > 0 is the rate constant. Because exponential models describe unbounded growth‚ they are unrealistic over long periods of time. Due to shortages of space and resources‚ all populations must eventually have decreasing grovtrth rates. Logistic growth models allow for exponential growth when the population is small

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  • PROPERTIES OF SINE AND COSINE FUNCTIONS

    PROPERTIES OF SINE AND COSINE FUNCTIONS: 1. The sine and cosine functions are both periodic with period 2π. 2. The sine function is odd function since it’s graph is symmetric with respect to the origin‚ while the cosine function is an even function since it’s graph is symmetric with respect to y axis. 3. The sine functions: a. Increasing in the intervals[0‚ π/2]and [3π/2‚ 2π]; and b. Decreasing in the interval [π/2‚ 3π/2]‚over a period of 2 π. 4. The cosine function is: a. Increasing in the interval

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  • Homework: Function and Graded Problems Math

    where m0 is the rest mass of the particle and c is the speed of light in a vacuum. Find the inverse function of f and explain its meaning. Solution. We simply solve for v: m= m0 1− v 2 /c2 =⇒ m 1 − v 2 /c2 = m0 =⇒ m2 1 − v2 c2 = m2 0 m2 v2 =⇒ 1 − 2 = 0 c m2 =⇒ v2 m2 =1− 0 c2 m2 m0 m m0 m 2 =⇒ v 2 = c2 1 − 2 =⇒ v = ±c 1 − Our new function v(m) gives velocity v as a function of m. In particular‚ v(m) gives the velocity (as measured by a relatively stationary observer) that

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  • Function and Inverse Cindy Dean

    Inverse In this week’s assignment‚ I will be solving functions with different values and variables. Many companies and businesses‚ use these methods to either make progress or to change something that will benefit their success. The first function is: (f – h)(4) f(4) – h(4) I multiplied 4 with each variable. f(4) = 2(4) + 5 The x is replaced with 4. f(4) = 13 I used the order of operation to evaluate this function. h(4) = (7 – 3)/3 I will repeat the steps that I used

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  • Variable Cost and Total Revenue Function

    BUSINESS MATHEMATICS: ASSIGNMENT - “Section” 5.1‚ page 182. (1) Write the general form of a linear function involving five independent variables. (2) Assume that the salesperson in Example 1 (page 177) has a salary goal of $800 per week. If product B is not available one week‚ how many units of product A must be sold to meet the salary goal? If product A is unavailable‚ how many units be sold of product B? (3) Assume in Example 1 (page 177) that the salesperson receives a bonus when combined

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  • Real World Quadratic Functions

    Real World Quadratic Functions Read the following instructions in order to complete this assignment: 1. Solve problem 56 on pages 666-667 of Elementary and Intermediate Algebra. 2. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay‚ please make sure to include: o An explanation of the basic shape and location of the graph and what

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  • Math Notes Logarithmic Functions

    and Logarithmic Functions 2.2 Logarithmic Functions MATH14 • Logarithmic Function with base b • Graph of Logarithmic Function • Natural Logarithmic Function • Properties of Logarithmic Functions • Exponential and Logarithmic Equations Logarithmic Function with base b Definition: The logarithmic function with base b is the inverse of the exponential function with base b. y  logb x Note: Dom  f   if and only if  x b y Rng  f   Logarithmic Function with base b Examples:

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  • Transfer Functions, Poles and Zeros

    HADNOUT E.13 - EXAMPLES ON TRANSFER FUNCTIONS‚ POLES AND ZEROS Example 1 Determine the transfer function of the mass-spring-damper system. The governing differential equation of a mass-spring-damper system is given by m x + c x + kx = F . Taking the Laplace transforms of the above equation (assuming zero initial conditions)‚ we have ms 2 X ( s ) + csX ( s ) + kX ( s ) = F ( s )‚ X ( s) 1 ⇒ = . 2 F ( s ) ms + cs + k Equation (1) represents the transfer function of the mass-spring-damper system. Example

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  • Trigonometric Functions and Exact Value

    6-1 Inverse Trig Functions p. 468: 1-31 odd I. Inverse Trig Functions A. [pic] B. [pic] C. [pic] Find the exact value of each expression 1. [pic] 2. [pic] 3. [pic] 4. [pic] 5. [pic] 6. [pic] Use a calculator to find each value. 7. [pic] 8. [pic] 9. [pic] Find the exact value of each expression. 10. [pic] 11. [pic] 12. [pic] 6-2 Inverse Trig Functions Continued p. 474:1-41

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  • Student Activity: a Generic Function

    Student Activity A Generic Function Use the generic graph of f(x) with domain [–6‚ –3] and [–2‚ 6] to answer the questions below. 7 Y 6 5 4 3 2 1 X -7 -6 -5 -4 -3 -2 -1 0 -1 1 2 3 4 5 6 7 -2 -3 -4 -5 -6 -7 1. What is the range of f(x)? 2. What is the domain? 3. On what intervals is f(x) decreasing? 4. On what intervals will the following statements be true? a) As x increases‚ y increases. b) As x increases

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