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Practice problems for exam 3 in math 107.04, focusing on solving equations, function modeling, trigonometry, and circles. Topics include using the quadratic formula to solve equations, constructing functions for bacterial population growth, evaluating trigonometric functions, finding the radius and area of a circular sector, and proving pythagorean identities.
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Math 107.04 Exam 3 Practice Spring 2009
(a) 73 x^ = 4x−^1 (b) 19 23 x^ − 4
= 3 (c) 2 + 3e^2 x^ − e^4 x^ = 0
(d) ex^ − 12 e−x^ − 1 = 0 (e) log 2 (x + 1) + log 2 (x − 2) = log 2 (3x)
(f) log 9 (x − 5) + log 9 (x + 3) = 1 (g) 2 log x = log(2x) − log(3x − 1)
n(t) = n 0 ekt
where t is measured in seconds.
(a) Construct a function that models the bacteria population after t seconds of light exposure.
(b) How long must the population be exposed to light to decline to 2 bacteria?.
n(t) = n 0 ekt
where t is measured in seconds.
(a) Construct a function that models the bacteria population after t seconds of immersion.
(b) How long must the population be immersed to grow to 240, 000 bacteria?.
(a) Find the radius of the circle. (b) Find the area of the circular sector.
(b) If θ in part (a) is in quadrant IV rather than quadrant I, which of the six trigonometric ratios found in (a) must change sign? Justify your answer.
(a) sin^2 θ + cos^2 θ = 1 (b) 1 + tan^2 θ = sec^2 θ (c) cot^2 θ + 1 = csc^2 θ
(a) cos θ, sin θ; θ in QIII (b) cot θ, csc θ; θ in QII (c) sin θ, sec θ; θ in QIV
for γ in QIV, find sin γ + cos γ.
(a) y = tan π 4
x (b) y = −4 sec
x +^5 π 6
(c) y = sec 2
x −
π 2
(d) y = −
3 csc^ π
x +
π 4
(e) y = tan
3 x^ −^
π 6
(f) y = − cot
2 x +
π 3
