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Unformatted text preview: MATH 122 PRETEST 1 This test is designed to give an example of what types of questions may be onlthe
test. Show all work for full credit. 1. The average weight in pounds of American men in their sixties (in 1979) as a,
function of their heights in inches is given in the following table. ‘ height(h) 70 71 72 73
weight(w) 166 171 176 181 186 191 a. How do you know from the table that weight w is a linear function of height h? b. What is the slope of the function? (Be sure to give units of measurement as part
of your answer.) c. Explain the meaning of the slope in terms of heights and weights. d. Find a formula that expresses the weight w in terms of the height h. 2 2. Complete the table of values for the linear function. a
—— Write the equation of this linear function. 3. Complete the table of values for the exponential function. u
——— Write the equation of this exponential function. 4. Suppose that y = x2 + m — 5. Find the average rate of change of y with respect
to a: over the interval 3 g a: S 6. 3 5. Find the equation of the linear function that passes through the points (3,12)
and (6, 48). 6. Find the equation of the exponential function that passes through the points
(3712) and (6,48). 7. The total cost 0 of producing 5r sneakers is given by the function
C(zc) = 0.01m2 — 0.250 + 2000. Find the average rate of change in the cost if production is increased from a: = 100
to :3 = 1.50. Give units. ' 4 8. A furniture company charges a ﬁxed amount plus a charge for each pound that
they move. A person who shipped 50 lbs of furniture was charged $300 while someone
else was charged $780 to move 210 lbs. a. Write a function that represents the moving cost, C, in terms of pounds, X. b. Find the vertical intercept and interpret it in relation to the problem. 9. A business discovers a linear relationship between the number of shirts it can
sell and the price per shirt. In particular, 12,000 shirts can be sold at $19 each, and
3,000 of the same shirts can be sold at $55 each. a. Write the number of shirts, S, as a function of the price, p, per shirt. b. What are the units of the slope? Interpret the meaning of the slope in everyday
language. c. Find the horizontal intercept and interpret it in relation to the problem. 5 10. In physics it is shown that the height 5 of a ball thrown straight upward with
an initial velocity of 80 feet per second from a rooftop 96 feet high is 3(t) = —16t2 + 8013 + 96 where t is the elapsed time that the ball is in the air. The ball misses the rooftop on the way down and eventually strikes the ground.
a. When does the ball strike the ground? b. Calculate the average velocity of the ball for its Whole trip to the ground. Give
units. 11. A population is growing according to the function P = 250(1065)‘7 where P is the population at year t.
a. What is the initial population? b. What is the annual growth rate? c. What is the population in 10 years? d. How many years will it take for the population to reach 1000? 6 12. Suppose an account earns interest at an annual rate of 9%, compounded continuously. Determine the amount of money grandparents must set aside at the
birth of their grandchild if they wish to have $20,000 by the grandchild’s eighteenth birthday. 13. Money deposited in a certain bank account doubles every 13 years. If the bank
compounds interest continuously, what annual interest rate does the bank offer? 14. A bakery has 250 lbs of ﬂour. If they use 12% of the available ﬂour each day,
how much do they have after one week? Write a formula for the amount of flour they have left after t days. 7 15. My husband and I have decided to start a mufﬁn company, Sanders’ Muffins.
We do some research and ﬁnd that we can rent a building for $1200 per month and
equipment for $395 per month, but we must sign a contract that even if we make no
mufﬁns, we are responsible for these rental fees. We buy our ingredients in bulk, so
we spend about $0.40 per mufﬁn for ingredients. We decide to sell our muffins for
$1.50 apiece. a. What is our cost equation, C, in terms of mufﬁns, m? b. What is the revenue equation, R, in terms of mufﬁns, m? c. What is the proﬁt equation, H,in terms of mufﬁns, m? d. How many mufﬁns do we have to sell to make a proﬁt? 8 16. The ﬁgure below gives both supply and demand curves for a certain economic
good. 1) (price indollmlitem) 0 1000 2000 3000 4000 5000 a. Why is the supply curve increasing as you move to the right? b. If the price is $50 per itemithe producers will supply ________ items. 0. Why is the demand curve decreasing as you move to the right? d. If the price is $50 per item, the consumers will buy ______ items. e. If the price is $50 per item, What would you predict about the future price of the
good? Explain. 9 . 17. What interest rate, compounded annually, is equivalent to a 7% rate com—
pounded continuously? 18. What interest rate, compounded continuously, is equivalent to a 7% rate com—
pounded annually? 19. If you invest your money in an account paying 4% interest per year, com
pounded annually, how long will it take for your money to double? 20. If 250mg of a radioactive element decays to 200mg in 48 hours, ﬁnd the half—life
of the element. 10 21. A bird species in danger of extinction has a population that is decreasing
exponentially. In the year 2000, the population was 1400, but by 20057 the population
was only 1000. Once the population drops to 100, the situation will be irreversible. When will this happen? 22. The half—life of cesium—137 is 30 years. How much 'of a 100—mg sample would
remain after 50 years? 23. Bank A offers 12% interest, compounded annually, and bank B offers 11.8%
interest, compounded continuously. You want to invest $1000 for 10 years. Which bank should you choose? Show your computations. 11 24. Solve for x. 25. For = 2932 — 2x and g(x) = 3m — 1, ﬁnd and simplify each of the following.
a f (900)) 26. Use the following table to ﬁnd each of the following. [an n
n
a f (9(8))
b 90%)) 12 27. The frequency, F, of a vibrating string is directly proportional to the square
root of tension, t. If a string vibrates at a frequency of 144 hertz due to a tension of 2 pounds, ﬁnd the frequency When the tension is 18 pounds. 28. Intensity of illumination from a light source is inversely proportional to the
square of the distance from the source. If the intensity of a light source is 100 lumens at a distance of 20 feet, ﬁnd the intensity at 30 feet. ...
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 Spring '08
 KUSTIN

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