Exam 2 Review-Chpts. 2&3 MTH 140
Precalculus
Name_____________________
1) 
2) 
3) Find
the coordinates of the vertex of the parabola given by 
4) The cost in millions of dollars for a
company to manufacture x thousand automobiles is given by the function 
. Find the number of
automobiles that must be produced to minimize the cost.
5) Graph the function using such
information as zeros and end behavior (without your calculator): 
6) A herd of bison is introduced to a
wildlife refuge. The number of bison, 
, after t years is described by the polynomial
function 
. Use the leading
coefficient to determine the graph’s end behavior. What does this mean about what will
eventually happen to the bison population?
7) Write the equation of a polynomial
function with the given characteristics:
Touches the x-axis at 0 and
crosses the x-axis at 2; lies above the x-axis between 0 and 2.
8) Find the domain of the rational
function 
.
9) Graph the rational function 
. Be sure to note any
asymptotes (horizontal, vertical, or slant) and any zeros.
10) Divide by long division: 
11) Find the slant asymptote, if any: 
12) A drug is injected into a patient and the
concentration of the drug is monitored.
The drug’s concentration, 
, in milligrams after t hours is modeled by: 
What is the horizontal asymptote,
and what does it represent?
13) Use the graph of the rational function
shown to complete the statement:
As 
14) Use the graph of the rational function
shown to complete the statement:
As 
15) Solve the quadratic inequalities. Express your solution sets in interval
notation.
a) 
b) 
16) Solve the rational inequalities. Express your solution sets in interval
notation.
a) 
b) 
17) The distance that an object falls when it
is dropped is directly proportional to the square of the amount of time since
it was dropped. An object falls 512 feet
in 4 seconds. Find the distance the
object falls in 5 seconds.
18) The power that a resistor must dissipate
is jointly proportional to the square of the current flowing through the
resistor and the resistance of the resistor.
If a resistor needs to dissipate 32 watts of power when 2 amperes of
current is flowing through the resistor whose resistance is 8 ohms, find the
power that a resistor needs to dissipate when 4 amperes of current are flowing
through a resistor whose resistance is 8 ohms.
19) Graph the function 
by making a table of
values.
20) Graph the exponential function 
, then use transformations of this graph to graph 
. Please include a
written explanation as part of your work, using phrases like “shifted ___ units
to the ____”.
21) Graph the exponential function 
, then use transformations of this graph to graph 
. Please include a
written explanation as part of your work, using phrases like “shifted ___ units
to the ____”.
22) Find the accumulated value of an
investment of $1000 at 12% compounded quarterly for 6 years.
23) Find the accumulated value of an
investment of $8000 at 8% compounded continuously for 3 years.
24) Write the equation 
in exponential form.
25)
Write the equation 
in logarithmic form.
26) Evaluate without using your calculator:
a) 
b) 
c) 
d) 
e) 
f) 
g) 
27) Find the domain of the function 
28) Use the properties of logarithms to
expand the following expressions as much as possible.
a) 
b) 
29) Use the properties of logarithms to
condense the following expressions as much as possible.
a) 
b) 
30) Use common or natural logarithms and a
calculator to find 
to four decimal
places.
31) Solve the following exponential
equations. Express the solution set both
in terms of natural logarithms and as a decimal rounded to the nearest
thousandths.
a) 
b) 
32) Solve the following logarithmic
equations. Give both the exact solution
and an approximate solution to 3 decimal places.
a) 
b) 
c) 
d) 
e) 
33) In the year 2000, you invested money in a
money market account. The value of your
investment t years after 2000 is given by the exponential growth model 
. When will the
account be worth $4502?
34) The logistic growth function 
describes the
population of a species of butterflies t months after they are
introduced to a non-threatening habitat.
a) How
many butterflies were initially introduced into the habitat?
b) What
is the limiting size of the butterfly population that the habitat will sustain?
35) According to the U.S. Bureau of the
Census, in 1980 there were 14.6 million residents of Hispanic origin living in
the 
describes the U.S.
Hispanic population, in millions, t years after 1980.
a) Find k, correct to 3 decimal places.
b) Use the resulting model to project the Hispanic resident population in 2005.
c) In what year will the Hispanic resident population reach 50 million?
Key
