Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
C Roettger, Spring 14
Name (please print): . . . . . . .
Math 181  Quiz 3A, related rates
Show your work. No notes or books. Time is 15 minutes. Please write
your name on the back and front of this paper.
Problem 1 Suppose the population P (t) satises P
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Practice exam 1  solutions
The real exam will be shorter, but there will be plenty of space on the
exam paper.
Problem 1 Stride length of humans S is roughly a linear function of
height H. Given the following data points, nd the equation for S
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Exam 1A  solutions
Problem 1 Assume there is a linear relationship between quantities H
and N , and you have obtained the following data.
Red alert  such an assumption must be justied if you want to
draw any conclusions from it!
8
H 2
N 20 3.
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Practice exam 1
The real exam will be shorter, but there will be plenty of space on the
exam paper.
Problem 1 Stride length of humans S is roughly a linear function of
height H. Given the following data points, nd the equation for S in terms
of
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Practice Exam 2  solutions
Problem 1 A population of dinosaurs produces ospring which numbers
P (t) = 0.3t2 +0.1t+10 for times t in the interval [4, 0]. At the same time,
dinosaurs die from various causes, deaths numbering D(t) = 0.2t2 + 0.1t
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Practice Exam 3  solutions
Problem 1 Consider the function
h(x) = (9x2 33x 25)e3x+1 .
a) Find h (x).
b) Find all critical numbers of h(x), and tell which of them is a relative
maximum and which a relative minimum (see 5.4, eg. p. 163).
Solutio
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
C Roettger
Name (please print): . . . . . . . . .
Math 181  Practice Questions for Final
Problem 1 The Northern Right Whale is one of the most endangered
marine mammals. Suppose that its population in the North Atlantic currently numbers 500 animals. Acc
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Practice Questions for Final solutions
Problem 1 The Asian Ladybird has been introduced in the US as biological pest control. Unfortunately, it does so well here that it outcompetes
native Ladybird species. Assume that a population of Ladybird
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
C Roettger
Name (please print): . . . . . . . . .
Math 181  Practice Questions for Final
Problem 1 The Asian Ladybird has been introduced in the US as biological pest control. Unfortunately, it does so well here that it outcompetes
native Ladybird speci
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
C Roettger
Name (please print): . . . . . . . . .
Math 181  Practice Exam 3
Problem 1 Consider the function
h(x) = (9x2 33x 25)e3x+1 .
a) Find h (x).
b) Find all critical numbers of h(x), and tell which of them is a relative
maximum and which a relative
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 1B, linear systems solutions
Problem 1 Solve the system
2a + b 2c = 6
4a + 3b + 6c = 0
a b + 5c = 0
Solution. There are many, many ways to do this! as an example, we
decide to eliminate b from I, II using III. So we write
I + III
II + 3III
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 2A, quick rules  solutions
Problem 1 Find the derivative of
f (x) = x6 + 3x4 + 2x2 + 4.
Solution.
f (x) = 6x5 + 12x3 + 4x
Problem 2 If f (a) = 3 and f (a) = 4, what is the derivative of
g ( x) =
4f (x) + 1
f (x) + 1
at x = a? use quick ru
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
C Roettger, Spring 14
Name (please print): . . . . . . .
Math 181  Quiz 3B, related rates
Show your work. No notes or books. Time is 15 minutes. Please write
your name on the back and front of this paper.
Problem 1 Suppose the population P (t) satises P
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 4B, exp/log equations solutions
Problem 1 Solve for t
4e0.3t 5e1.7t = 0.
Solution. Multiply both sides by e1.7t to get
4e2t 5 = 0
then isolate the exponential,
e2t =
5
4
Take ln on both sides to get
2t = ln
5
4
1
ln
2
5
4
and solve for t,
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 4A, exp/log equations solutions
Problem 1 Find all solutions for x of
x2 e4x 5xe4x = 14e4x .
Solution. Factor out e4x (alternatively multiply both sides by e4x ). This
factor is never zero, so we get
x2 5x 14 = 0
which can be factored as (
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 1A, linear systems solutions
Problem 1 Solve the system
2a + b 2c = 3
4a + 3b + 6c = 13
a b + 5c = 12
Solution. There are many, many ways to do this! as an example, we
decide to eliminate b from I, II using III. So we write
I + III
II + 3I
Calculus and Differential Equations for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Practice Exam 2
Problem 1 A population of dinosaurs produces ospring which numbers
P (t) = 0.3t2 +0.1t+10 for times t in the interval [4, 0]. At the same time,
dinosaurs die from various causes, deaths numbering D(t) = 0.2t2 + 0.1t in
the same