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 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.
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 ca
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Exam 1B  solutions
Problem 1 A patient has 5 milligrams (mg) per liter of a certain drug
in his bloodstream. The amount A(t) of the drug is measured every thirty
minutes. It decreases over
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 2B, quadratic models solutions
Problem 1 An oil spill grows over time. The area at time of the tth
measurement is At in square miles. Suppose A0 = 5, A1 = 8, A2 = 20 and
At = at2 + bt
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 1B, exponential
growth/decay  solutions
Problem 1 Algae mass per liter in a lake is measured every 2 days in
grams. The amount at time of the tth measurement is At . Suppose A0 = 2.5
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Exam 3  solutions
Problem 1 Consider the function
h(x) = x2 8x 6 ln(x).
a) Find h0 (x).
b) Find all values of x where h0 (x) is zero (critical values).
c) Tell which of the xvales in part
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 3A, natural domains solutions
Problem 1 Find the natural domain of the following functions (describe
in terms ofequations, inequalities, and/or words).
a) f (x) = x2 4
b) g(x) = x/(x2
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 2B, quadratic models solutions
Problem 1 An oil spill grows over time. The area at time of the tth
measurement is At in square miles. Suppose A0 = 4, A1 = 7, A2 = 19 and
At = at2 + bt
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Exam 1A  solutions
Problem 1 A patient has 5 milligrams (mg) per liter of a certain drug
in his bloodstream. The amount A(t) of the drug is measured every thirty
minutes. It decreases over
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 3B, natural domains solutions
Problem 1 Find the natural domain of the following functions (describe
in terms ofequations, inequalities, and/or words).
a) f (x) = x2 9
b) g(t) = 2t + l
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Quiz 1A, exponential
growth/decay  solutions
Problem 1 Algae mass per liter in a lake is measured every 2 days in
grams. The amount at time of the tth measurement is At . Suppose A0 = 2.5
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
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 f
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 fro
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 elimin
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
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 bot
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 p
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
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 eliminat
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 wh
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
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
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 i
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
Calculus and Mathematical Modeling for the Life Sciences I.
MATH 181

Spring 2014
Math 181  Exam 2A  solutions
Problem 1 The area of a mold colony is modeled for times t in the
interval [0, 5] by
A(t) = 0.3t2 + 4t + 1.
a) Find the rate of change of this area at t = 3.
b) Find the