Math 155. Homework 10. Sections 4.2 and 4.3.
1. Suppose that a bacterium is absorbing a certain drug from its environment. At time t = 0,
1 mol
there is 0.2 mol of drug in the bacterium, and drug enters the bacterium at a rate of 1+t2 min
(a) Let c(t) rep
Math 155. Homework 5. Sections 2.5, 2.6
Hold the Mayo!
Arterioclerosis and the Fourth-Power Relationship in the Hagen-Poiseuille Equation
After a worksheet by Todd Cooke, Professor of Biology, University of Maryland
Biological Motivation: From the website
Math 155
Exam 2
Fall 2012
NAME:
SECTION:
TIME:
INSTRUCTOR:
Instructions: The exam is closed book and closed notes. You may use an approved calculator,
but be sure to show your work on each problem for full credit. Work that is crossed out or erased
will n
Math 155
Final Exam
Fall 2012
NAME:
SECTION:
TIME:
INSTRUCTOR:
Instructions: The exam is closed book and closed notes. You may use an approved calculator,
but be sure to show your work on each problem for full credit. Work that is crossed out or erased
wi
Answers to Odd Exercises
863
the differential equation. The initial condition must have been
y (0) = 4.
13. With t = 1, x (1) = 1 + x (0) 1 = 1 + 0 1 = 1. With t =
0.5, the rst step is x (0.5) = 1 + x (0) 0.5 = 1 + 0 0.5 = 1.
The second step is x (1) = 1
Math 155. Calculus for Biological Scientists
Fall 2013
Course Website: www.math.colostate.edu/~shipman/math155
Please review the course website for details on the course and policies.
Living organisms grow, reproduce, and move around. They change. With Ca
Math 155. Homework 7. Sections 3.1 and 3.2.
1. Consider the following discrete-time dynamical system:
xt+1 = x2 + 7xt + 8
t
(a) Find the equilibria algebraically.
(b) Apply the Stability Test/Slope Criterion to each of the equilibria you found in (a). Wha
Math 155. Homework 8. Section 3.3.
1. Consider the function f (x) = x3 6x2 + 10 on the interval [1, 7].
(a) Calculate f (x), and use this to nd all the critical points of f (x).
(b) Calculate f (x), and use this to nd regions where f (x) is concave up or
Math 155
Exam 1
Spring 2012
NAME:
SECTION:
TIME:
INSTRUCTOR:
Instructions: The exam is closed book and closed notes. You may use an approved calculator,
but be sure to show your work on each problem for full credit. Work that is crossed out or erased
will
Answers to Odd Exercises
843
10
Final value
8
6
4
2
0
0
2
4
6
Initial value
8
10
3. At the lower equilibrium, the updating function crosses the diagonal from below to above and is therefore unstable. At the
upper equilibrium, the updating function crosses
Answers to Odd Exercises
Chapter 1
11. f (a ) = a + 5, f (a + 1) = a + 6, f (4a ) = 4a + 5.
Section 1.2, page 21
13. h
1. The variables are the altitude and the wombat density, which
we can call a and w, respectively. The parameter is the rainfall,
which
Answers to Odd Exercises
826
3. With
With
With
With
4.02.
h
= 6.0.
t
h
t = 0.5, h = h (1.5) h (1.0) = 2.5, so
= 5.0.
t
h
t = 0.1, h = h (1.1) h (1.0) = 0.42, so
= 4.2.
t
h
t = 0.01, h = h (1.01) h (1.0) = 0.0402, so
=
t
t = 1.0,
h = h (2.0) h (1.0) = 6.0,
Graphing Trigonometric Functions
f (t) = A + B cos
2
T (t
)
0. You may have to rewrite the formula to express it in the above standard form (example on
other side).
1. A: average value
3. : phase
5. Add the standard cosine squiggle
2. B : amplitude; A +
M ath
NAME:
E xam L
1 55
F all2OO7
l ./
1 1er t
I
TIME:
SECTION:
INSTRUCTOR:
The exarn is closed book and closed notes. You may use an
fnstructions:
approved calculator, but be sure to show your work on each problem for full
credit. Work that is crossed o
Math 155. Homework 11. Sections 4.4 and 4.5.
1. A plant produces starch depending on the intensity of heat it receives during the day. Assume
the rate of starch production of the plant is
4t
dS
=
grams per hour
dt
1 + t2
where time t is measured in hours