 # MAT 142 College Mathematics

## Question:

All assignments must be typed, and the work should be clearly displayed.

Electronic graphs are preferred over hand-drawn.

You can find directions to graph using Excel on the blackboard.

You can ask for help with assignments.

Consumer Price Index.

The table below shows the consumer price index (CPI) as compiled by U.S. Department of Labor.

Year

Write a paragraph on the Consumer Price Index.

Make sure to describe it.

Find the average change in consumer price index between 2010-2015.

Include a sentence to explain what your answer means.

Find the average change of the consumer price index between 2012-2013. Include a sentence to explain what your answer means.

Profit Functions.

A company can list its profit function.

x is measured in thousands while P is measured in dollars.

The function should be graphed.

Only include the area that is relevant to a profit function in your graph.

For example, x cannot be negative since you cannot sell or make a negative number.

Find the average rate at which profit changes from x =100 to x=200.

Create a sentence to interpret 2b.

Include the correct units. Interpret part b of the graph in part A.

Consumer price index (CPI).

Mankiw, 2014, at p.212.

It is a weighted average price of certain goods and services, such as food and health care.

CPI’s change can be used to measure price changes linked to the cost of living.

It can also be used as an economic indicator for inflation in a particular region within a certain time period (Dwivedi (2005)).

Calculate the average change of the consumer price index between 2010-2015.

Please include a sentence to explain what your answer means.

Year

Average Change =

According to (Stewart2012; Marjit2011), the average change of CPI in relation to x can be found at. Where y1andx1are initial values, and respectively y2andx2are final values.

Accordingly, the average CPI increase will be shown by

Sum of all the changes in the table above

Find out the average change in consumer price index from 2012-2013

Include a sentence to explain what your answer means

The formula in the b column will be used

= 1.32% annually

This suggests that the CPI has increased by 3 Dollars in one-year from 2012.

In one year, the average price of consumer products has increased by 1.32%.

Profit function

The average profit change rate is between x = 100 and x = 200. This is done by multiplying the profit change by inx

Write a sentence to interpret 2b.

This rate of change in profit is 3 dollars per 1 unit of product.

This means that if x increases by 1 unit, profit for the company will increase 3.

Part b is the part that you should interpret in part a.

It is clear from the chart that the profit rose by 100 units when the x was increased by 100 units.

This means the profit is three times as much as the change in x units (200-100=100).

References

Principles of macroeconomics.

Basic calculus: Transcendentals in the early years.

Macroeconomics theory and policy.

Tata McGraw-Hill Education.

India: SAGE Publications.

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