Modeling the Dynamics of Life: Calculus...3rd EditionFrederick R. Adler Publisher: Cengage LearningISBN: 9780840064189
Modeling the Dynamics of Life: Calculus...
Solutions for Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
Problem 1E:
Identify the variables and parameters in the following situations, give the units they might be...Problem 3E:
Compute the values of the following functions at the points indicated and sketch a graph of the...Problem 4E:
Compute the values of the following functions at the points indicated and sketch a graph of the...Problem 5E:
Compute the values of the following functions at the points indicated and sketch a graph of the...Problem 6E:
Compute the values of the following functions at the points indicated and sketch a graph of the...Problem 7E:
Graph the given points and say which point does not seem to fall on the graph of a simple function....Problem 8E:
Graph the given points and say which point does not seem to fall on the graph of a simple function....Problem 9E:
Graph the given points and say which point does not seem to fall on the graph of a simple function....Problem 10E:
Graph the given points and say which point does not seem to fall on the graph of a simple function....Problem 11E:
Evaluate the following functions at the given algebraic arguments. f(x)=x+5 at x=a,x=a+1, and x=4a.Problem 12E:
Evaluate the following functions at the given algebraic arguments. g(y)=5y at y=x2,y=2x+1, and y=2x.Problem 26E:
Find the inverses of each of the following functions. In each case, compute the output of the...Problem 30E:
Graph each of the following functions and its inverse. Mark the given point on the graph of each...Problem 31E:
Graph each of the following functions and its inverse. Mark the given point on the graph of each...Problem 32E:
Graph each of the following functions and its inverse. Mark the given point on the graph of each...Problem 34E:
Find the compositions of the given functions. Which pairs of functions commute? f(x)=2x+3 and...Problem 53E:
The following series of functional compositions describe connections between several measurements....Problem 54E:
The following series of functional compositions describe connections between several measurements....Browse All Chapters of This Textbook
Chapter 1 - Introduction To Discrete-time Dynamical SystemsChapter 1.2 - Variables, Parameters, And Functions In BiologyChapter 1.3 - The Units And Dimensions Of Measurements And FunctionsChapter 1.4 - Linear Functions And Their GraphsChapter 1.5 - Discrete-time Dynamical SystemsChapter 1.6 - Analysis Of Discrete-time Dynamical SystemsChapter 1.7 - Expressing Solutions With Exponential FunctionsChapter 1.8 - Oscillations And TrigonometryChapter 1.9 - A Model Of Gas Exchange In The LungChapter 1.10 - An Example Of Nonlinear Dynamics
Chapter 1.11 - An Excitable Systems: The HeartChapter 2 - Limits And DerivativesChapter 2.1 - Introduction To DerivativesChapter 2.2 - LimitsChapter 2.3 - ContinuityChapter 2.4 - Computing Derivatives: Linear And Quadratic FunctionsChapter 2.5 - Derivatives Of Sums, Powers, And PolynomialsChapter 2.6 - Derivatives Of Products And QuotientsChapter 2.7 - The Second Derivative, Curvature, And AccelerationChapter 2.8 - Derivatives Of Exponential And Logarithmic FunctionsChapter 2.9 - The Chain RuleChapter 2.10 - Derivatives Of Trigonometric Functions
Book Details
Designed to help life sciences students understand the role mathematics has played in breakthroughs in epidemiology, genetics, statistics, physiology, and other biological areas, MODELING THE DYNAMCICS OF LIFE: CALCULUS AND PROBABILTY FOR LIFE SCIENTISTS, Third Edition, provides students with a thorough grounding in mathematics, the language, and 'the technology of thought' with which these developments are created and controlled. The text teaches the skills of describing a system, translating appropriate aspects into equations, and interpreting the results in terms of the original problem.
Sample Solutions for this Textbook
We offer sample solutions for Modeling the Dynamics of Life: Calculus and Probability for Life Scientists homework problems. See examples below:
Given information: The functions, f(x)=2x+3 and g(x)=3x−5 . Formula used: The addition of the...Given information: The functions, f(x)=2x+3 and g(x)=3x−5 . Formula used: The multiplication or...Given information: The functions, f(x)=2x+3 and h(x)=−3x−12 . Formula used: The multiplication or...Given information: The functions, F(x)=x2+1 and G(x)=x+1 . Formula used: The multiplication or...Given information: The functions, F(x)=x2+1 and H(x)=−x+1 . Formula used: The multiplication or...Given information: The population of people is P(t)=2.0×106+2.0×104t.............(A) The mass per...Given information: (f?g)(×) and (g?f)(×) if f(×)=sin(×) and g(×)=x2 Calculation: Given that the...Given information: The height of the first tree is h1=23.1m and the height of the second tree is...Given information: The height of the first tree is h1=23.1m and the height of the second tree is...
Given information: The height of the tree h is given by, h=100a100+a ,where a represents the age of...Given: The function F(r)=r2+5 The given input points are as follows: r=0 r=1 r=4 Consider the...Given information: The table that provides elevation of the surface of Great Salt Lake in Utah for...Given information: The table that provides relation between measurement of a growing plant. Age, a (...Given information: The table that provides relation between measurement of a growing plant. Age, a (...Given information: The table that provides relation between measurement of a growing plant. Age, a (...Given information: The table that provides relation between measurement of a growing plant. Age, a (...Given information: The discrete-time dynamical system of medication concentration Mt+1=0.75Mt+2.0...Given: The discrete- time dynamical system for volume: Mt+1=0.75Mt+2.0 The initial condition is...Given: The discrete- time dynamical system for volume: Mt+1=0.75Mt+2.0 The initial condition is...Given: The given updating function is h(x)=xx−1 The initial condition is x0=3 Calculation: The...Given information: b0=3.0×106 bacteria Calculation: Suppose a population of bacteria with the...Given: The population of bacteria doubles every hour but that 1.0×106 individual are removed before...Given information: The discrete time dynamical system, xt+1=axt1+xt . Formula used: The steps to...Given information: The discrete time dynamical system, xt+1=xtxt−K . Formula used: The steps to...Given: The equation is, bt+1=0.5bt+100 starting from b0=100 Calculation: Let initial be b0 . The...Given: The discrete-time dynamical system : Mt+1=12Mt+1 Consider the following discrete-time...Given: The equation, 4e−2x+1=7e3x . Concept Used: Laws of Logs: Law 1: Product property of...Given: The equation, 4e2x+3=7e3x−2 . Concept Used: Laws of Logs: Law 1: Product property of...Given: The given function is 0.1e−0.2x Calculation: The graph of the function will be The value of x...Given information: D=cM−34 Calculation: Consider the following function: D=cM34 Here, D is the...Given information: S1(t)=3.4e0.2t. Calculation: We are to find the doubling time and plot graph to...Consider the following functions: S1(t)=3.4e0.2tS2(t)=0.2e3.4tH1(t)=3.4e−0.2tH2(t)=0.2e−3.4t The...Given information: Given ln(x) is 10≤x≤100,000 Graph: The value of ln(x) is 10≤x≤100,000 . The graph...Given: θ=0 Concept Used: cos(0)=1 Calculation: To check the identity cos(θ2)=1+cosθ2 At θ=0 Put θ=0...Given: θ=0 Concept Used: sin0=0, and cos(0)=1 Calculation: To check the identity sin2θ+cos2θ=1 At...Given: θ=0 Concept Used: cos(0)=1, and sin(0)=0 Calculation: To check the identity...Given: θ=0 Concept Used: cos(0)=1, and sin(0)=0 Calculation: To check the identity sin(2θ)=2sinθcosθ...Given information: Consider the following functions,...Given : It is given in the question that the volume of the lungs is V , the amount breathed in and...Given : It is given in the question that the the volume of the lungs is V , the amount breathed in...Given : It is given in the question that the volume of the lungs is V , the amount breathed in and...Given : It is given in the question that the the volume of the lungs is V , the amount breathed in...Given information: 3.0×106m3 Calculation: We ate given that there is no evaporation in the lake and...Given information: Suppose that a fraction 0.1 of wild-type mutate each generation, but that each...Given information: Suppose that a fraction 0.2 of wild-type mutate each generation, but that each...Given information: Each year, 20% of the butterflies from the first island fly to the second and 30%...Given information: Each year, 20% of the butterflies from the first island fly to the second and 30%...Given: The given parameter is, Vc=20.0 mVu=10.0 mVc=0.7Vt=30.0 mV Calculation: The potential of the...Given: The parameters are, Vc=20.0 mVu=10.0 mVc=0.4, 0.9, 1Vt=30.0 mV Calculation: The potential of...Chapter 1, Problem 1SPGiven: Given the functions f(x)=e−2xg(x)=x3+1 Calculation: First find the inverse of f(x) Let f(x)=y...Given information: θ=60∘ Calculation: Let us convert the angles from degree to radian by using the...Given information: b(t)=1.5t Calculation: Consider the equation for a population size. b(t)=1.5t The...Given information: b(t)=2.0t Calculation: Consider the following equation for a population size....Given information: h(t)=5.0t2 Calculation: Consider the following equation for a population...Given information: b(t)=(1.0+2.0t)3 Calculation: Consider the equation for population size....Given information: f(x)=5x2 near x=1 . Formula used: Average rate of change = f(x+Δx)−f(x)Δx Concept...Given information: f(x)=5x2+7x+3 near x=1 . Formula used: Average rate of change = f(x+Δx)−f(x)Δx...Given information: f(x)=5x2+7x+3 near x=2 . Formula used: Average rate of change = f(x+Δx)−f(x)Δx...Given: Inside the sun the temperature increases by approximately 1 million C0=106 C0 for every...Given information: The function h(y)=y2ln(y−1) for y>1 . Formula used: If a function f is...Given information: The function r(w)=(1−w)−4 . Formula used: If a function f is continuous at a...Given information: A continuous function that is −1 for x≤−0.1, 1 for x≥0.1 and is linear for...Given information: A continuous function that is −1 for x≤−0.01, 1 for x≥0.01 and is linear for...Given information: The given quadratic function is f(x)=4−x2 . Method/Formulaused: The slope of a...Given information: The given quadratic function is g(x)=x+2x2 . Method/Formulaused: The slope of a...Given: The given function is y(t)=10t2.5 . Base point is t=1 and secant joins the base point t=1 and...Given information: The volume of a sphere as a function of radius r is given by V(r)=4π3r3 . We have...Given: A population of bacteria consists of two types a , b which grow with time according to...The above- ground volume (stern and leaves) of a plant represented by the following equation....Given information: The series of polynomials is given as follows....Given: The given functions are, f(x)=2x+3g(x)=−3x+2 Calculation: Consider the following function,...Given: The given functions are, f(x)=x2+2g(x)=3x2−1 Calculation: Consider the following function,...Given: The population size is P(t)=2.0×106+1000t2 The weight per person is W(t)=80−0.5t Calculation:...Given: The given mass function M(t) and the volume function V(t) are: M(t)=1+t2 and V(t)=1+2t ,...Given information: The function g(z)=z+1z . Formula used: Let a function g be continuous on closed...Given information: The function h(x)=(1−x)(2−x)(3−x) . Formula used: Let a function g be continuous...Given information: The function M(t)=t1+t . Formula used: Let a function g be continuous on closed...Given information: The function f(x)=10x2−50x . Formula used: Let a function g be continuous on...Given: The function, F(z)=1+e−z1+ez . Concept Used: The quotient rule of derivatives:...Given: The function, p(x)=1−ex1+ex . Concept Used: The quotient rule of derivatives:...Given information: The function F(z)=z3ez and domain 0≤z≤5 . Graph: Consider the provided function...Given information: The given function is G(x)= e−xx , the graph to be shown in the interval 0≤x≤2 ....Given: F(x)=(1+2x)3 Concept Used: Addition/subtraction rule of differentiation formula...Given information: The function, q(x)=x+x2 for x≥0 . Formula used: Let a function g is...Given information: The given implicit relation is y2+4xy+4x4=0 , the slopes of tangents at points...Given: The speed of the Cheetah is 30m/s towards the popular watering hole and the misguided gazelle...Given information: Consider the equation E=c1(pM)0.75+c2((1−p)M)0.75...Given information: The function c(z)=e−zsin(z) and the points 0,π2 and π . Formula used: The slope...Given information: The function p(t)=et(1+0.2cos(t)) and the points 0,π2 and π . Formula used: The...Given: The given equation is d2ydt2=−sin(y(t)) And the solution of the spring equation is...Given: The expression is cos(cos(x)) . Calculation: The critical point is the point on the curve...Given: limx→0(1+x2) Concept Used: Theorem on limits: limx→a[f(x)g(x)]=limx→af(x)limx→ag(x), product...Given: The volume of a cell as a function of time is given by V(t)=2−2t+t2 , V(t) (in 1000 s of μm3...Given information: Consider the equation, x(t)=2.0cos(2πt3.2) Calculation: The position of the...Given information: Consider the equation with increasing temperature, Vi(t)={T if T≤50100...
More Editions of This Book
Corresponding editions of this textbook are also available below:
EBK MODELING THE DYNAMICS OF LIFE: CALC
3rd Edition
ISBN: 9781285225975
EBK MODELING THE DYNAMICS OF LIFE: CALC
3rd Edition
ISBN: 9780100452565
EBK MODELING THE DYNAMICS OF LIFE: CALC
3rd Edition
ISBN: 8220100452567
Modeling The Dynamics Of Life: Calculus And Probability For Life Sciences
3rd Edition
ISBN: 9781285119076
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