. Here is a linear demand function: Q = 10 -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.

                                                                                                          P =

 

                                                                                                           TR=

 

2. Evaluate the following expression. Y = 5X²Â +4X +6   EXAMPLE: When X = 2, Y = 44.

 

a. When X = 0, Y = ___                                            b. When X = 5, Y = ___

c. When X = 3, Y = ___                                            d. When X = 0.5, Y = ___

 

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

 

1.  X^-1/5, When X = 2, this gives ____.
2.  X¹, When X = 4, this gives ____.
3.  X^1/2, When X = 64, this gives ____.
4.  X^3/4, When X = 2, this gives ____.
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6. 4. 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 = 3X²Â -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.
7. a. Y = 4X²Â +4X -8. The two roots are X = ______ and X = ______.
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12. b. Y = 5X²Â +X -6. The two roots are X = ______ and X = ______.
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19. 5. 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:
20.            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)¹²Â -1 = 0.0121 or 1.21% annually.
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24.            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?
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28.            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. 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?
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32.            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/e^rt 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?
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Status NEW Posted 12 Jul 2017 02:07 AM My Price 20.00

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