1.Here is a linear demand function:Q = 30 -10P.Find its price function by inverting the demand function.Then find its total revenue function by multiplying through by Q.EXAMPLE:The linear demand function Q = 400 -250P inverts into the price function P = 1.6 -0.004Q.Multiplying this by Q gives its total revenue function TR = 1.6Q -0.004Q².This skill will be useful in assignment 4.Show the algebra involved.

a.Derive the price function from the demand function Q = 30 -10P:

P =

b.Derive the total revenue function from your price function in (a):

TR =

2.Evaluate the following TR function: TR = 3Q - 0.1Q². EXAMPLE: When Q = 15, TR = $22.50.

a.When Q = 10, TR = $______b.When Q = 30, TR = $_____

3.Evaluate the following expression.Y = 3X + 5(X + 2)² EXAMPLE:When X = 1, Y = 48.

a.When X = 0, Y = ___b.When X = 2, Y = ____

c.When X = 3, Y = ___d.When X = 5, Y = ____

4.Evaluate the following exponentials.You may need to use a calculator with a Y^x key.EXAMPLE:X ^-1/4.If X = 16, this gives _0.5__. Compute all to two decimal places or more.

a.X^-1/3, When X = 3, this gives ____.

b.X⁰, When X = 2, this gives ____.

c.X^1/3, When X = 3, this gives ____.

d.X^3/2, When X = 4, this gives ____.

5.Find the two roots of each of the following quadratic functions (that is find the two X values making Y = 0).This skill may be useful in assignment 11.Example:Y= 3X² -11X +6 is the product of (3X -2)(X - 3).If you let Y = 3X-2 then X = 2/3 will make Y = 0.If you let Y = X -3 then X = 3 will make Y = 0.Thus both X = 2/3 and X = 3 are roots. Show the algebra involved.

a. Y = 2X² -2X -12.The two roots are X = ______ and X = ______.

b.Y = 2X² + X -15.The two roots are X= ______ and X = ______.

6. Exponential functions are useful in business and economics.Lesson 7 discusses them. Show how the values are entered into your functions and also calculate the amounts for each of the following:

a1. You learn on the business channel that inflation was about 0.2% last month.Assume this rate is maintained each month for a year.What will the annualized rate be?EXAMPLE: A rate of 0.1% per month represents (1 + 0.001)¹² -1 = 0.0121 or 1.21% annually.

a2. Suppose you set a goal of 5% sales growth for the year.What monthly growth rate would this require, assuming a level (the same) average rate for each month?EXAMPLE: A 2% growth rate for the year would require 1.02 = (1 + r)¹².Solve this for r:; r = .00165 or .165% per month on average.

b1. F = Pe^rt , which assumes continuous compounding, says that the Future value (F) of an amount (P) invested today at an annual rate (r), expressed as a decimal for the time (t), in years is given by the function (assuming continuous compounding).EXAMPLE:invest $100 at the annual rate of 5 1/2% for 6 years and 3 months and you should get back (at the end of the time), F = $100e^{(0.055)(6.25)} = $100e^(0.3438) = $100(1.4102) = $141.02.If you deposit $10000 today into your saving account, what amount would you have in 10 years if it can earn 6% per annum?

b2.Alternatively,P = F/e^rt.P tells you the most you should loan.EXAMPLE: A borrower tells you that he will give you back $141.02 at the end of a loan that for 6 years and 3 months with an interest rate of 5 1/2% per annum.The most you should have loaned him was P = $100. Here is a loan proposition more in line with current interest rates.A borrower agrees to pay you 4 3/4% annually for 7 years and 6 months.At the end of the term, he will make a balloon payment of $20000 to repay the loan and the interest.What amount (P) should loan this prospect?