exponential

Satisfactory Essays
Topics: Time, Forecasting, Future
Exponential Smoothing Forecasting Method with Naïve start
Formula: Ft = α (At-1) + (1 – α) (Ft – 1) where:

Ft Forecast for time t

Ft – 1 Past forecast; 1 time ahead or earlier than time t At-1 Past Actual data; 1 time ahead or earlier than time t

α (read as alpha) as a smoothing constant takes the value between 0 and 1; or has value of either 0.1 to 0.9. With value more than 0 .5 (categorized as high), it gives more weight to recent data; with value less than 0.5 (categorized as low), it gives more weight to past data. With value equal to 0.5, forecast is giving emphasis on the past 3 periods; With value equal to 0.1, there is little weight on recent data and more on Past, about 19 periods in the past.

Naïve start is used in absence of forecast data. It is the actual prior period data to period t.

Sample Problem: Estimate the rate of increase in yield of mushroom for April and May in a given controlled field if the rate of increases in January and subsequent months are given below and other variables are same or constant:

Naïve Actual Data % Forecast January 10 - February 12 10 March 13

You May Also Find These Documents Helpful

  • Good Essays

    Exponential function

    • 2230 Words
    • 9 Pages

    In mathematics, the exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex is its own derivative.[1][2] The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable. The function is often written as exp(x), especially when it is impractical to write the independent variable as a superscript…

    • 2230 Words
    • 9 Pages
    Good Essays
  • Satisfactory Essays

    Exponential Function

    • 2732 Words
    • 11 Pages

    Identify the choice that best completes the statement or answers the question. ____ 1. Tell whether the function y = 2( 5 ) shows growth or decay. Then graph the function. a. This is an exponential growth function. c. This is an exponential decay function. x b. This is an exponential growth function. d. This is an exponential growth function. ____ 2. Graph the inverse of the relation. Identify the domain and range of the inverse. x y −1 4 1 2 3 1 5 0 7 1 a. c. Domain: {x | 0 ≤ x ≤ 4}; Range:…

    • 2732 Words
    • 11 Pages
    Satisfactory Essays
  • Good Essays

    Exponential Funtions

    • 354 Words
    • 2 Pages

    Exponential Functions An exponential function is in which a constant base is raised to a variable power. Exponential functions are used to model changes in population size, in the spread of diseases, and the growth of investments. They can also accurately predict types of decline typified by radioactive decay. The essence of exponential growth, and a characteristic of all exponential growth functions, is that they double in size over regular intervals. The most important exponential function is…

    • 354 Words
    • 2 Pages
    Good Essays
  • Powerful Essays

    G Exploring Exponential Models 1 x 3. y 5 2 Q 5 R Graph each function. 1. y 5 (0.3)x 6 Date 2. y 5 3x y 6 y y 4 4 2 2 x x Ϫ2 O 2 Ϫ2 O 2 x Ϫ2 O 1 4. y 5 2(3)x 5. s(t) 5 2.5t y 6 s(t) 6 f(x) 4 2 4 6 4 1 6. f (x) 5 2(5)x 2 2 2 Ϫ2 O x t x 2 1 x 7. y 5 0.99 Q 3 R decay; 0.99 Ϫ2 O Ϫ2 O 2 2 Without graphing, determine whether the function represents exponential growth or exponential…

    • 505 Words
    • 3 Pages
    Powerful Essays
  • Good Essays

    LOGARITHMIC AND EXPONENTIAL FUNCTIONS Inverse relations Exponential functions Exponential and logarithmic equations One logarithm THE LOGARITHMIC FUNCTION WITH BASE b is the function y = logb x. b is normally a number greater than 1 (although it need only be greater than 0 and not equal to 1). The function is defined for all x > 0. Here is its graph for any base b. Note the following: • For any base, the x-intercept is 1. Why? To see the answer, pass your mouse over the colored…

    • 3127 Words
    • 13 Pages
    Good Essays
  • Good Essays

    EXPONENTIAL AND LOGARITHMIC FUNCTIONS I.EXPONENTIAL FUNCTION A. Definition An exponential function is a function defined by f(x) = ax , where a > 0 and a ≠ 1. The domain of the function is the set of real numbers and the range is the set of positive numbers. B. Evaluating Exponential Functions 1. Given: f(x) = 2x, find a. f(3) = ____ b. f(5) = _____ c. f(-2) = ______ d. f(-4) = ______ 2. Evaluate f(x) = ( 1)x if 2 a. x = 2 ____ b. x = 4 _____ c. x = -3 ______ d…

    • 904 Words
    • 4 Pages
    Good Essays
  • Satisfactory Essays

    Exponential and Logarithmic Functions * Verify that the natural logarithm function defined as an integral has the same properties as the natural logarithm function earlier defined as the inverse of the natural exponential function. Integrals of Exponential and Logarithmic Functions Function | Integral | lnx | x ∙ lnx - x + c | logx | (x ∙ lnx - x) / ln(10) + c | logax | x(logax - logae) + c | ex | ex+c | ek∙x | 1 / k ∙ ek∙x + c | ax | ax / lna + c | xn | 1 / (n+1) ∙ xn+1 +…

    • 361 Words
    • 2 Pages
    Satisfactory Essays
  • Satisfactory Essays

    21. Optimization 2 Test 3 22. Exponential Functions 23. Logarithmic Functions 24. Compound Interest 25. Differentiation of Exponential Functions 26. Differential of Logarithmic Functions 27. Exponential Functions as Mathematical Models…

    • 338 Words
    • 3 Pages
    Satisfactory Essays
  • Satisfactory Essays

    MATH133 Unit 5: Exponential and Logarithmic Functions Individual Project Assignment: Version 2A Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols. IMPORTANT: See Question 1 in Problem 2 below for special IP instructions. This is mandatory. Problem 1: Photic Zone Light entering water in a pond, lake, sea, or ocean will be absorbed or scattered by the particles in the water and its intensity, I, will be attenuated…

    • 1387 Words
    • 9 Pages
    Satisfactory Essays
  • Good Essays

    Exponential Functions in Business Turgenbayeva Aiida ID 20092726 Variant 2 Kazakhstan Institute of Management, Economics and Strategic Research MSC1101 Mathematics for Business and Economics Instructor: Dilyara Nartova Section #2 Summer-I 2009 Abstract This project reflects my knowledge and understanding of the interest rate, its types, formula and its evaluation in order to determine the most profitable type of investment scheme for National Bank wishing to increase…

    • 908 Words
    • 4 Pages
    Good Essays