1. Here is a linear demand function: 0.3Q = 12 - 3P. 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 0.3Q = 12 - 3P:

P=

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

TR =

2. Evaluate the following TR function: TR = 4Q - 0.1Q2. EXAMPLE: When Q = 20, TR = $40.

a. When Q = 10, TR = $____ b. When Q = 40, TR = $_____

3. Evaluate the following expression. Y = 5X2 +4X +6 EXAMPLE: When X = 2, Y = 34.

a. When X = 0, Y = ___ b. When X = 1, Y = ___

c. When X = 2, Y = ___ d. When X = 4, Y = ___

4. Evaluate the following exponentials. You may need to use a calculator with a Yx key. EXAMPLE: X -1/4. If X = 4, this gives _0.7071__. Compute to two decimal places or more.

X-1/5, When X = 2, this gives ____.

X1, When X = 4, this gives ____.

X1/2, When X = 64, this gives ____.

X3/4, When X = 2, this gives ____.

5. Find the two roots of each of the following functions (that is find the two X values that make 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 = 4X2 +4X -8. The two roots are X = ______ and X = ______.

b. Y = 5X2 +X -6 . 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 of each of the following:

a1. You learn on the business channel that inflation was about 0.8% 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. Your sales grew 4% last year. 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. What average monthly growth rate is needed to give the 4% growth?

b1. F = Pert , 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. Thus if you invested $100 now at the annual rate of 5 1/2% for 6 years and 3 months you would get back (at the end of the time), F = $100e(0.055)(6.25) = $100e(0.3438) = $100(1.4102) = $141.02. Suppose you put $2000 in a savings account when your son was born for 18 years and 6 months to help pay for his college education. If you can earn 3% annually on it, what should you have in his education savings account in 18 years and 6 months?

b2. Alternatively, if a borrower tells you that he needs a loan for 6 years and 3 months and will pay you an annual rate of 5 1/2% for the loan, but will give you only $141.02 back at the end of the loan term , you should only loan him $100 today. What amount does the formula P = F/ert indicate that you need to place in a savings account today in order to have $150,000 by the time your daughter goes off to college in 18 years and 6 months if the account earns 3% annually?