1). Show that L (x) = log₃x is an inverse of E(x) = 3^x using:

• the theorem L(E(x)) = E(L(x))= x
• By graphing at the same axis.

2). The revenue of a company during last 20 years recorded at the table below:

year, ( x) revenue, y (in thousands of dollars

2000 1020

2001 915

2003 905

2005 815

2006 750

2009 705

2010 890

2011 870

2012 920

2015 950

2017 1040

2018 1100

2019 1120

2020 1150

Find/Describe the following:

a). Draw the Scatter Diagram. What makes you think that the data

could/should represent a parabola, why or why not?

b). Find the quadratic equation that best fit the revenue of that

company over last 20 years. Interpret the concavity of the quadratic

function and identify whether the vertex represent the

maximum/minimum revenue of that company.

c). Using the predicted function, find and describe when the company will

have its maximum/minimum revenue.

d). Find then describe the maximum/minimum revenue of that company.

e). Identify any two years when the company will have same revenue using

the predicted quadratic function above.