Suppose that the previous forecast was 2090 and the actual value of the variable of interest for the period was 1985 and the oldest value of interest was 1955. Using the moving average technique based upon the most recent four observations find new forecast for the next period.
To use the moving average technique to forecast the next period, we'll calculate the average of the most recent four observations, which are 2090, 1985, the value before that, and the one before that. Then, we'll use this average _____ _____ ____ ___ ____ ____ ___ _____ ______ _____ __________ __________.
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Classify the following into linear and non-linear models, justifying your classification.
i) Simple harmonic motion for small amplitude of oscillation.
ii) Population growth model given by are constants.
iii) Equation for velocity v of a particle at any time t, moving with a constant acceleration a, and initial velocity u.
iv) Equation describing dynamic stability of market equilibrium price given by are constants and
is the price in period t.
Compare the phase diagrams of the systems:
i)
ii)
by locating the equilibrium points and sketching the phase paths.
A particle moving in .H.S M has got the velocities cm8 /sec and cm6 /sec when it is at distance cm3 and cm4 respectively from the centre of its motion. Determine the period and the amplitude of motion.
Consider the epidemic model governed by the following equation
with initial condition x = n at t = 0 . Here )t(x is the number of susceptibles at time ,t β is the contact rate. The population is assumed to be closed and homogeneously mixing. Let the contact rate be 0.002 and the number of susceptibles be 5000 initially
i) Find the density of the population when the rate of appearance of new cases is maximum.
ii) Find the time (in weeks) at which the rate of appearance of new cases is maximum.
iii) Obtain the maximum rate of appearance of new cases.
Given all the portfolios of n securities what criterion would an investor use to select a good portfolio?
A parachutist, whose weight (actually mass) is 64 kg, drops from a helicopter 5000 m. above the ground. She falls towards the earth under the influence of gravity. Assume that the gravitational force is constant. Assume that the force due to air resistance is proportional to the velocity of the parachutist. The proportionality constant is sec when the parachute is closed, and is sec
when it is open. If the parachute does not open until 1 minute after the parachutist leaves the helicopter, after how many seconds will she hit the ground?
Consider the following system of equations
Find the nature of the critical point ,0( of the corresponding linear system.