#1. (12 points) On a college campus, one student returnedfrom vacation with a contagious flu virus. The

spreadof the virusthroughthestudentbodyis givenby p(t) =;OOt , wheretis the numberof days

2t + 32

that have passed since the student has returned to campus and p(t) is the percentage of students who have

the flu at that time.

a) What percentage of the students have the flu after one week?

b) Find lim p(t) .

t-oo

c) Explain what your answer in part b) tells you in the context of this problem.

#2. (12 points) Let f(x) =2x3 +.JX +6.

a) Find J'(x).

b) Findf(2x3 +£ + 6)dx.

c) Find fJ'(x)dx.

#3. (26 points) Let f(x) =X4-4x3 + 5 . Answer the questions below; show your work clearly.

a) Use calculus to determine the intervals where the function is increasing or decreasing.

b) Use calculus to determine the intervals where the function is concave upward or concave downward.

c) List the coordinates of all of the relative maximumpoints of the graph of the function (if there are

none, write "none").

d) List the coordinates of all of the relative minimumpoints of the graph of the function (if there are

none, write "none").

e) List the coordinates of all of the points of inflectionof the graph of the function (if there are none,

write "none").

1

#4. (14 points) Evaluate the integralfx(x2 + 1)3dx using a suitable substitution.

4

#5. (16 points) Given f(x) =\

(2x + 1), find J'(x). You do not need to simplify your answer.

3- 5x

#6. (14 points) Bismuth-210 has a half-life of 5.0 days. A sample Bismuth-210 originally has a mass of

800 mg.

a) Find a formula of the form Q(t) =Qoe-kt for the mass remaining after tdays (in particular, you need

to find Qoand k).

b) Find the mass remaining after 30 days.

#7. (14 points) Let f(x) =(x2- 9)3. Use calculus to find the coordinates of the absolute maximum point on

the graphof fon theinterval-4 s xs 1.