This assignment covers topics such as consumer price index, average change in CPI, profit function, and average rate of change in profit. It includes calculations, graphs, and interpretations. The subject is Mathematics, and there is no specific course code, course name, or college/university mentioned.
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Running Head: Math Assignment Mathematics Assignment Student’s Name Institution Affiliation
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Running Head: Math Assignment Question One A.Consumer price index(CPI) “is measure of overall cost of goods and services purchased by a regular consumer”(Mankiw,2014, p.212). It evaluate the weighted average prices of set of goods and services purchased regularly by people each year, for example food and health care services. A change in CPI is used to evaluate the price changes that are linked to cost of living.It’s also used as an economic indicator of inflation in a given region at within a given period of time(Dwivedi,2005) B.Findingthe average change in the consumer price index from 2010 to 2015. Include a sentence that explains what your answer means. Data: YearCPIAverage Change= Object 2 2010$217 2011220 *100=1.38 2012227 *100=3.18% 2013230 *100=1.32% 2014234 *100=1.74% 2015234 *100=0%
Running Head: Math Assignment The average change in CPI between two years is given by. According to (Stewart 2012;Marjit2011), average change of y in relation to x is given by , where y1and x1 are initial values and y2 and x2 are final value, Therefore, for average change in CPI will be given by Sum of all changes determined in the table above Average change will be given by =1.39+3.18+1.32+1.74+0=7.62% This indicates that the price of consumer goods has averagely increased by 7.62% in five years. C.Find the average change in the consumer price index from 2012 to 2013 Include a sentence that explains what your answer means The formula in b will be applied = 1.32% per year This suggest that the CPI increase by 3 dollars over one year from 2012. Averagely the price of the consumer products have increased by 1.32% in one year.
Running Head: Math Assignment Question two Profit function P(x) = 6x – 0.01x2– 500 A.Graph the function 50100150200250300350400450500550 0 50 100 150 200 250 300 350 400 450 Grapgh of P(x) B.average rate of change in profit fromx = 100tox = 200. This is given by change in profit divide by in x X Px
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Running Head: Math Assignment C.Write a sentence interpreting 2b. This rate of change of profit is 3 dollar per 1 unit of product x. This means that when x increases with 1 unit, the profit of the of the company will increase by 3. D.Interpret part b on the graph in part a From the chart inait’s clear, when the x increase by 100 unit the profit increased from 0 to 300 dollars. This means that the profit is three times the change in x units( 200-100=100)
Running Head: Math Assignment References Mankiw, N. G. (2014).Principles of macroeconomics. Cengage Learning. Stewart, J. (2012).Essential calculus: Early transcendentals. Cengage Learning. Dwivedi, D. N. (2005).Macroeconomics: theory and policy. Tata McGraw-Hill Education. Marjit, S. (Ed.). (2011).India Macroeconomics Annual 2010. SAGE Publications India.