Mathematics for Life Sciences Study Guide
Questions
Course Introduction
Mathematics for Life Sciences introduces students to the essential mathematical concepts and techniques used to analyze biological systems and processes. The course covers topics such as modeling population dynamics, rates of change, probability, statistics, and the application of calculus to biological phenomena. Emphasis is placed on interpreting quantitative data, constructing and analyzing mathematical models, and applying mathematical reasoning to real-world problems in fields such as ecology, genetics, physiology, and epidemiology. This course provides a vital foundation for students pursuing studies or careers in biology, medicine, environmental science, and related disciplines.
Recommended Textbook
Calculus An Applied Approach 10th Edition by Ron Larson
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11 Chapters
1279 Verified Questions
1279 Flashcards
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Page 2
Chapter 1: Functions, graphs, and Limits
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427 Verified Questions
427 Flashcards
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Sample Questions
Q1) To help their son buy a car on his 16th birthday,a boy's parents invest $1,900 on his 10th birthday.If the investment pays an annual rate of 9% compounded continuously,how much is available on his 16th birthday? Round your answer to the nearest cent.
A) $3,240.96
B) $3,260.41
C) $3,186.49
D) $2,926.00
E) $16,475.16
Answer: B
Q2) The measurement of the circumference of a circle is found to be 54 centimeters,with a possible error of 0.7 centimeters.Approximate the percent error in computing the area of the circle.
A) 3.70 %
B) 1.30 %
C) 2.59 %
D) 5.19 %
E) 1.85 %
Answer: C
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3
Chapter 2: Differentiation
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84 Flashcards
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Sample Questions
Q1) The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long?
A) 96 ft<sup>2</sup>/min
B) 1,008 ft<sup>2</sup>/min
C) 504 ft<sup>2</sup>/min
D) 2,016 ft<sup>2</sup>/min
E) 84 ft<sup>2</sup>/min
Answer: B
Q2) A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place.
A) -24.1 feet/second
B) -0.2 feet/second
C) -0.6 feet/second
D) -15 feet/second
E) -0.9 feet/second
Answer: D
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Chapter 3: Applications of the Derivative
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122 Verified Questions
122 Flashcards
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Sample Questions
Q1) The measurement of the circumference of a circle is found to be 54 centimeters,with a possible error of 0.7 centimeters.Approximate the percent error in computing the area of the circle.
A) 3.70 %
B) 1.30 %
C) 2.59 %
D) 5.19 %
E) 1.85 %
Answer: C
Q2) A travel agency will plan a tour for groups of size 53 or larger.If the group contains exactly 53 people,the price is $800 per person.However,each person's price is reduced by $10 for each additional person above the 53.If the travel agency incurs a price of $150 per person for the tour,what size group will give the agency the maximum profit?
A) 6
B) 91
C) 59
D) 70
E) 32
Answer: C
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5
Chapter 4: Exponential and Logarithmic Functions
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122 Verified Questions
122 Flashcards
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Sample Questions
Q1) The number of a certain type of bacteria increases continuously at a rate proportional to the number present.There are 100 present initially,and 200 present 6 hours later.How many will there be 20 hours after the initial time? Round your answer to the nearest integer.
A) 10 bacteria
B) 903 bacteria
C) 1,008 bacteria
D) 23 bacteria
E) 18 bacteria
Q2) What is the annual percentage yield (or effective annual rate)for a nominal rate of 8.7% compounded quarterly? Round your answer to two decimal places.
A) 8.70%
B) 9.06%
C) 9.09%
D) 8.99%
E) 8.89%
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6
Chapter 5: Integration and Its Applications
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Sample Questions
Q1) A ball is thrown vertically upwards from a height of 6 ft with an initial velocity of 40 ft per second.
How high will the ball go?
A) 29.03 ft
B) 29.34 ft
C) 30.89 ft
D) 25.02 ft
E) 32.12 ft
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Chapter 6: Techniques of Integration
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Sample Questions
Q1) Present Value of a Continuous Stream of Income.An electronics company generates a continuous stream of 4t income of million dollars per year,where t is the number of years that the company has been in operation.Find the present value of this stream of income over the first 15 years at a continuous interest rate of 10%.Round answer to one decimal place.
A) $407.2 million
B) $176.9 million
C) $497.3 million
D) $1296.3 million
E) $324.1 million
Q2) Suppose the mean height of American women between the ages of 30 and 39 is 64.5 inches,and the standard deviation is 2.7 inches.Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 feet 4 inches and 6 feet tall.
A) 0.5734
B) 0.5707
C) 0.8547
D) 0.9522
E) 0.4257
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Page 8
Chapter 7: Functions of Several Variables
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113 Verified Questions
113 Flashcards
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Sample Questions
Q1) Determine whether the statement is true or false.If it is false,explain why or give an example that shows it is false.
A linear regression model with a positive correlation will have a slope that is greater than 0.
A)True
B)False
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Chapter 8: Trigonometric Functions
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60 Verified Questions
60 Flashcards
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Sample Questions
Q1) A compact disc can have an angular speed up to 3,154 radians per minute.At this angular speed,how many revolutions per minute would the CD make? Round your answer to the nearest integer.
A) 1,004
B) 1,577
C) 402
D) 502
E) 251
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Chapter 9: Probability and Calculus
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36 Flashcards
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Sample Questions
Q1) Three people are asked their opinions on a political issue.They can answer Opposed (O)or Undecided (U).Find the sample space S.
A) {OOO, OOU, OUO, UOO, UUU, UUO, UOU}
B) {OOO, OOU, UOO, UUU, UUO, UOU, OUU}
C) {OOO, OOU, OUO, UOO, UUO, UOU, OUU}
D) {OOO, OUO, UOO, UUO, UOU, OUU}
E) {OOO,OOU,OUO,UOO,UUU,UUO,UOU,OUU}
Q2) A coin is tossed three times.Describe the event A that at least two tails occur.
A) {TTT, THH, THT, HHT}
B) {HHH, TTH, THT, HTT}
C) {TTT, TTH, THT, HTT}
D) {TTTT, TTHT, THTT, HTTT}
E) {TT,HT,TH}
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11
Chapter 10: Series and Taylor Polynomials
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104 Flashcards
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Sample Questions
Q1) You accept a job that pays a salary of $60,000 the first year.During the next 49 years,you will receive a 6% raise each year.What would be your total compensation over the 50-year period? Round your answer to the nearest integer.
A) $17,420,154
B) $1,000,000
C) $56,400
D) $360,000
E) $3,600
Q2) Find the next three terms of the geometric sequence 8,40,200,....
A) 232, 264, 296
B) 1,000, 5,000, 25,000
C) 360, 520, 680
D) 205, 210, 215
E) 200,1,000,5,000
Q3) What are the next three terms in the arithmetic sequence -2,-6,-10,....
A) -14, -18, -22
B) 2, 6, 10
C) 56, -224, 896
D) -8, -10, -12
E) -10,-14,-18
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Chapter 11: Differential Equations
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77 Flashcards
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Sample Questions
Q1) The rate of change of the population of a city is proportional to the population P at any time (in years).In 2000,the population was 200,000,and the constant of proportionality was 0.015.Estimate the population of the city in the year 2020.
A) 260,972 people
B) 268,972 people
C) 263,972 people
D) 266,972 people
E) 269,972 people
Q2) A population of eight beavers has been introduced into a new wetlands area.Biologists estimate that the maximum population the wetlands can sustain is 60 beavers.After 3 years,the population is 15 beavers.The population follows a Gompertz growth model.How many beavers will there be in the wetlands after 10 years?
A) 34 beavers
B) 32 beavers
C) 30 beavers
D) 31 beavers
E) 39 beavers
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13