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Unformatted text preview: Math 130 Final Exam Spring 2009 Directions: Do not simplify unless indicated. Non-graphing calculators are permitted. Show all work
as appropriate for the methods taught in this course. Partial credit will be given for any work, words
or ideas which are relevant to the problem. Please put problem 1 on answer sheet 1 1. (a) Find the intercepts and vertex of the function f = ~33? + 6x — 5 and use them to sketch
the graph. Label your points with their coordinates. b Find the equation of the line passing throu h the point 3, —4 and perpendicular to the line
y = —2x + 7. Write this in slope-intercept form. (0) Suppose the price of a textbook is a linear function of the year. In 1980 a textbook cost $20
and every three years resulted in a cost increase of $2.50. i. Find a linear function which gives the cost of a textbook in the year t. Write this in
slope—intercept form. ii. When will a textbook cost $100? Please put problem 2 on answer sheet 2 2. (a) Find the domain of y = V 1+1 + \/ 10 ~ 1r. Write your solution in interval notation. £17
(b) If f = 2 — i ﬁnd and simplify the expression —f(x+hf)l‘f(m),
(c) Find but do not simplify % 25in(w2)_
Please Put problem 3 on answer sheet 3 x2+2 3. (a) Find lim 4z_1. (b) Solve 8”” = (yam-H without using logarithms. (c) Suppose a population of monkeys grows by 42% each year. How long will it take to triple?
Give an exact answer and an approximation to two decimal digits. Please put problem 4 on answer sheet 4 4. (a) Find the equation of the line tangent to the graph of f = x10g3 x at m = 9. (b) A} certain drug is injected into the bloodstream and immediately begins to decay exponentially. Suppose 0.7mL are injected and 8 hours later only 0.4mL remains. Find a
function Q(t) which gives the quantity of the drug at time t in hours and use this function
to determine how much will remain one full day from the injection. Give an exact answer
and an approximation to two decimal digits. Continues on Other Side [10 pts] [5 pts] [5 pts]
[5 pts] [10 pts]
[5 pts] [7 pts] [8 pts]
[10 pts] [10 pts]
[15 pts] Please put problem 5 on answer sheet 5 5. (a) Solve for % where 11f1(:vy)+y2 = x - y (b) A certain’s person blood pressure is given by the function 1
t = 11 ' —
p() 0+30s1n1607r (t+ 160) Where p(t) is measured in mmHg (a pressure measurement) and t is in minutes. Sketch the
graph of p(t) and then point out (With an arrow) where the blood pressure is maximum.
Label this point with its coordinates. This graph should not be drawn to scale. Please put problem 6 on answer sheet 6 6. (a) Find $1331 9811/: . (b) Use the limit deﬁnition to ﬁnd % (2 — . . . . d 3
(c) Use the llmit deﬁnition to ﬁnd 5 53-1.
Please put problem 7 on answer sheet 7 7. (a) Suppose the population of bacteria in a culture after [t days is given by 300
P“) z 1 + 26—00% Find and interpret P(7) and P’ Give exact answers and approximations to two decimal
places. (b) Find and use all of: m-intercepts, y-intercept, increasing/decreasing7 relative extrema,
and concavity to sketch the graph of h(x) = $275 — x Remember: Organized work is more important than the graph. The graph is worth 5 pts. Please put problem 8 on answer sheet 8 8. (a) Find the (absolute) extrema of the function f on the interval [—3, O] for ﬂa—12 1 “ﬁ$+§ (b) Suppose you are fencing in a rectangular area of dimensions L x W. The lengths cost $20/ft while the Widths cost $10/ft. The area must be 1000ft2. Find
the dimensions Which will minimize the cost. Make sure you justify why your answer is a
minimum. The End [10 pts] [15 pts] [8 pts] [7 pts]
[10 pts] [10 pts] [15 pts] [10 pts] [15 pts] . .. 7y_.__w——q~ﬁ ...
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- Spring '08