Math 220, Sections 01**, T Pilachowski, Spring 2006
April 6, 2007 MATH 220 – TEST 2(B) (3.1 – 5.4) [Pilachowski]
Follow directions carefully:
• Use exactly ONE answer sheet per question (use the back of the sheet if needed).
• Put your name, your TA's name, the question number, and a big letter B on EACH page.
• No books, notebooks, calculators, cell phones or other electronic devices.
• Put a BOX around the final answer to a question.
• Show enough work that we can follow your thinking. You must show all appropriate work in order
to receive full credit for an answer.
• Before handing in your test: on your first answer sheet only, please copy the pledge and sign.
ANSWERS SHOULD BE EXACT AND IN SIMPLEST FORM UNLESS OTHERWISE INDICATED.
Answer question 1 on answer page 1.
1. a. ( 12 points) Given the function
() ( )
13 2−−= x
exxm , find the x-coordinates of all extrema, and
determine whether each is a maximum or minimum.
b. (12 points) Find the first derivative of
() ()
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
+
=12
2
ln 2
xe
x
xp x. Simplify your answer, if possible.
You do not need to add fractions together.
c. (14 points) Zenestra’s investment of $500 three years ago is now worth $700. If it continues to grow
in value at the same rate, how much will it be worth eight years from now? Give both an exact value
answer and a decimal approximation to the nearest penny.
d. (6 points) The number of deer in a forest is modeled by the equation
()
t
e
tP 3
5
30
−
+
=. What is the
maximum number of deer the forest can sustain?
Answer question 2 on answer page 2.
2. The amount of a medicinal drug in a patient’s bloodstream is modeled by
()
(
)
t
etQ 03.0
45 −
−= , where
Q is measured in mg and t is time in hours since the initial dose. (Exact value answers for all parts.)
a. (4 extra points) What was the amount of the initial dose?
b. (6 points) How much of the drug is in the patient’s bloodstream after 2 hours?
c. (8 points) How quickly is the amount of the drug changing after 2 hours?
Answer question 3 on answer page 3.
3. a. (6 points) Write the expression
(
)
2
53 xx ee −
•in the form kx
e.
b. (12 points) Find the first derivative of
()
1
3
22
+
+
=x
e
ex
xh . You must have all the correct pieces in the
right places, but do not need to simplify.
c. (14 points) Find the second derivative of
()
1
3+
=x
exg . You must simplify, but you do not need to
factor.
d. (10 points) Solve
()
1ln1ln =−+ xx . Hint: At some point you’ll need to factor to solve this one.