Time and Date Stamps (logged): 17:12:20 06-10-2020
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Precalculus II
Precalculus I Final Exam
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Test should be printed using Internet Explorer. If
printed from different browser check to be sure test items have not been cut off. If
items are cut off then print in Landscape Mode (choose File, Print, click on Properties
and check the box next to Landscape, etc.).
Name and Signature of Student
_____________________________
Signed by Attendant, with Current Date and Time:
______________________
If picture ID has been matched with student and name as
given above, Attendant please sign here: _________
Instructions:
- Test is to be taken without reference to text or
outside notes.
- Graphing Calculator is allowed, as is blank paper or
testing center paper.
- No time limit but test is to be taken in one
sitting.
- Please place completed test in Dave Smith's folder,
OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va.,
24212-0828 OR email copy of document to dsmith@vhcc.edu,
OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..
Directions for Student:
- Completely document your work.
- Numerical answers should be correct to 3 significant
figures. You may round off given numerical information to a precision consistent
with this standard.
- Undocumented and unjustified answers may be counted
wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or
yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get
partial credit. So show your work and explain your reasoning.
- Due to a scanner malfunction and other errors some
test items may be hard to read, incomplete or even illegible. If this is judged by
the instructor to be the case you will not be penalized for these items, but if you
complete them and if they help your grade they will be counted. Therefore it is to
your advantage to attempt to complete them, if necessary sensibly filling in any
questionable parts.
- Please write on one side of paper only, and staple
test pages together.
Test Problems:
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Problem Number 1
What are the basic points of the exponential function y = f(x) = 7 * e^( 1.52 x)? Graph
the function using these points.
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Problem Number 2
What quadratic function describes the behavior of the graph of y = p(x) =
(x- 3)(x- 3)(x+ 4.3) near the point ( 3,0)?
- Compare the values of this function and p(x) at x = 3-1, 3-.5, 3-.1, 3+.1,
3+.5 and 3+1.
- Sketch the quadratic function and p(x) at these values of x.
- How does the quadratic approximation to p(x) deteriorate as x gets further and
further from the zero x = 3?
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Problem Number 3
The population of a certain organism is governed by the recurrence relation a(0)
= 2, a(1) = 4, a(n) = a(n-1) + 4 a(n-2), where n is the number of the population
transition.
- Find the populations after each of the first 10 transitions.
- Find the ratios a(n) / a(n-1) for n = 3, 4, ..., 10. Fully describe the
behavior of the ratios.
- What would you expect to be the growth factor for an exponential function
f(n) = A b^n which models the population for large values of n?
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Problem Number 4
If f(x) = .52 x + -4.005 and g(x) = 5.526 x^2 + 2.089 x - .52, sketch graphs of f(x) and
g(x). Show how you combine the graphs to obtain the graph of f(x) / g(x).
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Problem Number 5
State the laws of exponents, and give an example of each.
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Problem Number 6
If a sound measures 100 decibels, then what is the intensity of the sound, as a
multiple of the hearing threshold intensity?
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Problem Number 7
What will be the maintenance level of a drug, given
a dose of 800 mg with 50 % of the drug removed between doses?
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Problem Number 8
Linearize the data set consisting of the weight (pounds) vs. time (years) points
( 7, 4), ( 10, 6.14), ( 13, 9.424) and ( 16, 14.467).
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Problem Number 9
Find within .1 year the doubling time for an investment which gives an annual
rate of return of 6.3%, and compare to the doubling time when the rate is doubled.
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Problem Number 10
A graph of the range r(y) of a water stream coming from a hole in the side of a
container, as a function of water depth y, is a power function r(y) = k `sqrt(y) with
r-intercept (0,0) and graph point ( 65, 16). A graph of the depth y(t) as a function
of clock time t, in seconds, is approximated by a parabola with its y-intercept at
(0, 25) and vertex at ( 113 , 0 ).
- Sketch reasonable graphs of these functions and use the graphs to construct the
function r(t) which gives stream range as a function of clock time.
- From estimates and interpretations of appropriate slopes on the graphs of r(y)
and y(t) estimate the slope of your r(t) graph at t = 25 and give the interpretation of
this slope.