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1)The increasing value of a 1909 Honus Wagner baseball card in 2007 was $2.35 million. The value of the card has followedthe exponential growth model V with t = 0 corresponding to 1990 and V is calculated in millions of dollars:
a)What does the number 0.451 represent in our model? Include units in your answer.
b)Will the value for “k” be positive or negative? Explain why.
c)Find the value of “k”.
d)What will the value of the card be in 2017?
e)In what year will the card have a value of $5 million?
Calculations / Pointsa)The initial value of $451,000 or $0.451 million
b)K will be positive, because the value of the card has increased (exponential growth)
c)
d)The value of the card in 2017 is $6,205,000.00
e)
The card will have a value of $5 million in 2014. / a)1: Answer
b)
c)
d)1: Answer
e)
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2. A fishing boat heading due south is about to turn towards one of two docks. Dock 1 is located at a bearing of S 47° W of the boat. Dock 2, which is 15 km due east of Dock 1, has a bearing of S 52° E of the boat. Round all calculations to three decimal places.
a)Draw a diagram for the situation. Be sure to include all information provided.
b)Which dock is the boat closer to? How much closer is the boat to this dock than to the further dock?
c)A dock worker spots a swimmer hanging onto a buoy that is 3 km away from Dock 1. The buoy has a bearing of N 24° W from the dock. How far would the fishing boat have to travel to rescue the swimmer?
Calculations / Points
a)b)Distance from Boat to Dock 1 (side a):
km
Distance from Boat to Dock 2 (side b):
km
Dock 1 is closer to the boat by 1.007 km.
c)
/ a)
b)
c)
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3.Given the function.
a)Find the domain of f(x) in interval notation.
b)Find the equation(s) of the vertical asymptote(s) if they exist.
c)Find the equation(s) of the horizontal or slant asymptote(s) if they exist.
d)Determine the zero(s) of f(x) if they exist. Show the computations you used to arrive at your answer.
e)Sketch the graph of f(x) on the axes below in the interval [-10, 10]. Be sure to show the asymptote(s), zero(s), and any other important feature(s).
Calculations / Pointsa)Domain:
b)Vertical Asymptote: x = 3
c)Horizontal Asymptote: y = 1
d)Zero:
e)
/ a) 1: Answerb)1: Equation
c)1: Equation
d) 1: Answer
e)
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4. Find all the solutions to the following trigonometric equations in the interval .
a)
b)
Calculations / Pointsa)Solve for x
b)Solve for x by factoring
Apply Zero – Product Property
/ a)
b)
Pre-Calculus with Trig – Formative Practice (FR)Form BPage 1 of 5
School Year 2014-2015 Rev. 10.14