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- What is the index formulation used for?It is projected that in the future, the population of a certain country in millions will be P(t)= 85e^.05t, where t is is time in years since 2022. Round all answers to the nearest whole number a. What is the projected population of the town in 2026 b. Find the simplified derivative function c. At what rate will the population be changing in 2026 d. In what year was the population increasing at a rate of 5 million people per year e. When will the population reach 160 millionWhat conditions must non-linear time series models, such as vector autoregressive models, satisfy in order to use impulse response functions
- Q3 Please solve with hand by calculation using formulas (not in excel)Alternative Measures of Productivity A common measure of productivity, as explained in thischapter and as used by many business and trade organizations, including the U.S. Bureau of LaborStatistics, is the ratio of output to input, where input is typically measured in units of materials, laborhours, or related measures. An alternative is to use the ratio of capacity available to capacity utilized. For example, the amount of capacity in the U.S. manufacturing industries has almost doubledover the past two decades. However, the rate of capacity utilization (output/capacity available) hasfallen slightly over this period of time, with a steep drop in 2009 followed by slow increases in 2010and 2011. Some would say that this measure gives a better picture of productivity than the one wehave used in the chapter.Required Compare the measure of productivity based on capacity utilization with the measure used inthe chapter. Which measure do you think is most useful for assessing the state of the…Q6 Suppose that at time t=0, half of a "logistic" population of 100000 persons have heard a certain rumor and that the number of those who have heard it is then increasing at the rate of 500 persons per day. How long will it take for this rumor to spread to 80% of the population? ( Suggestion: Find the value of k by substituting P(0) and P'(0) in the logistic equation) a. About 98 days b. About 34 days c. About 19 days d. About 69 days e. About 119 days
- A town has a population of 5000 persons, but is expected to grow by 2% every year. (i) What wound be the population size in 7 years? (ii) Find the sum of the first eight terms of the sequence 1/8,−1/4 ,1/2,.... Please show working.Use this method, Exponential decline model, to solve ( in petroleum economics) The production of the oil well decline exponentially, the initial flow rate is 1500 STB/day, the production rate of this well become 120 STB/day in the fourth year, find the production rate after 25 months from the beginning, find yearly production and production rate for this well for the next 4 years?Plot the logarithm of arrivals for each transportation mode against time, all on the same graph. Which now appears to be growing the fastest?
- The forecasting staff for the Prizer Corporation has developed a model to predict sales of its air-cushioned-ride snowmobiles. The model specifies that sales S vary jointly with disposable personal income Y and the population between ages 15 and 40, Z, and inversely with the price of the snowmobiles P. Based on past data, the best estimate of this relationship is S=kYZP where k has been estimated (with past data) to equal 100. If Y=11,000,Z=1,200, and P=20,000, what value would you predict for S? What happens if P is reduced to $17,500? How would you go about developing a value for k? What are the potential weaknesses of this model?Estimate the double-log (log linear) time trend model for log cruise ship arrivals against log time. Estimate a linear time trend model of cruise ship arrivals against time. Calculate the root mean square error between the predicted and actual value of cruise ship arrivals. Is the root mean square error greater for the double log non-linear time trend model or for the linear time trend model?Q2B. Which of the following are limitations of using Impulse Response Functions(IRFs) in time series analysis?i. IRFs are only valid for linear time series models.ii. IRFs assume that the underlying time series is stationary.iii. IRFs can provide information about the short-term dynamics of the relationshipbetween variables, but they do not capture longer-term effects or otherimportant aspects of the relationship.iv. IRFs depend on the specification of the model used to estimate the relationshipbetween variables.