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1
10 Distance Learning
Final E
x
am
Summer 2012
Due: Thursda
y
, 8/9/2012 at 11:55PM. After that time you will receive 0 for this exam.
Show your work to receive full credit. When using your calculator, write down what you used for inputs (functions stored in Y1 or Y2, window settings, input values for STAT or the Solver, etc.) and also indicate which features of the calculator you used (QuadReg, value, etc.).
1. The following table gives the size and cost of a line of Samsung LCD HDTV televisions.
|
Screen size (inches) |
23 |
27 |
32 |
|
Cost ($) |
250.00 |
340.00 |
420.00 |
(a) Name your variables (x, y, etc.) and find the best fitting linear model. (Round coefficients to the nearest hundredth.)
(b) What is the significance of the slope? Give a full explanation.
(c) Use your model to estimate the cost of the new 42 inch television.
2. Mike was playing golf at Hartford Golf Club. He hit the shot from the 4th tee which was 7 yards above the ground level. Mike’s shot took a quadratic flight. At a horizontal distance of 60 yards from the 4th tee, the height of his ball was 32 yards. His shot landed at 200 yards from the tee in a sand trap (ground level). Let x be the horizontal distance from the 4th tee and y be the height.
(a) What is the function of the flight of his ball? (Please round to 2 decimal places).
(b) Sketch a graph of the equation from a). Be sure to give ranges for the x- and y- axes.
(c) How high did his shot go?
(d) What is the significance of the y-intercept?
3. The sleeping aid Ambien has a biological half-life of about 1.5 hours. Assume someone takes a 10 mg dose at 9:00 p.m.
(a) Find an exponential model for the amount of Ambien in the person’s body x hours after 9:00 p.m.
(b) What is the decay rate?
(c) How much Ambien will be left at 10:00pm?
(d) Estimate how long it takes for amount of Ambien to reach 2 mg.
4. Harry decided to save money for his new born son’s college cost right now. He wants to have $120,000 in 18 years. Bank of America has a program paying 2.5% interest rate compounded monthly. Harry has two options. Option A, deposit a big amount of money now and withdraw it after 18 years. Option B, deposit a small amount of money at the end of every month for 18 years.
(a) For option A, how much does he need to deposit now?
(b) How much total interest will he receive for option A?
(c) For option B, what is his monthly payment?
(d) How much total interest will he receive for option B?
5. A person collects coins (nickels, dimes, and quarters) in a jar. At the end of the year they emptied the jar and found that there were 110 coins. The value of all the coins was $11.20. If there were twice as many dimes as quarters, how many of each type of coin were there?
a) Define the variables needed to solve the problem
b) Set up a system of equations modeling the facts.
c) Find the solution by solving the system of equations in b) using rref on your calculator (show the original matrix and the row-reduced matrix). No credit will be given for simply guessing the answer.
6. Graphs of the following four equations are shown below.
y = a x2 + b x + c , y = k (q)x , y = m x + d , y = p x3 + r
a) Find the values for c, k, m, d, and r.
b) Determine whether a and p are positive or negative.
c) Determine whether q is greater than 1 or less than 1.
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