 1.3.1: Under the same assumptions that underlie the model in (1), determin...
 1.3.2: The population model given in (1) fails to take death into consider...
 1.3.3: Using the concept of net rate introduced in 2, determine a model fo...
 1.3.4: Using the concept of net rate introduced in 2, determine a model fo...
 1.3.5: A cup of coffee cools according to Newtons law of cooling (3). Use ...
 1.3.6: The ambient temperature Tm in (3) could be a function of time t. Su...
 1.3.7: Suppose a student carrying a flu virus returns to an isolated colle...
 1.3.8: At a time denoted as t 0 a technological innovation is introduced i...
 1.3.9: Suppose that a large mixing tank initially holds 300 gallons of wat...
 1.3.10: Suppose that a large mixing tank initially holds 300 gallons of wat...
 1.3.11: What is the differential equation in 10, if the wellstirred soluti...
 1.3.12: Generalize the model given in equation (8) on page 23 by assuming t...
 1.3.13: Suppose water is leaking from a tank through a circular hole of are...
 1.3.14: The rightcircular conical tank shown in Figure 1.3.12 loses water ...
 1.3.15: A series circuit contains a resistor and an inductor as shown in Fi...
 1.3.16: A series circuit contains a resistor and a capacitor as shown in Fi...
 1.3.17: For highspeed motion through the airsuch as the skydiver shown in ...
 1.3.18: A cylindrical barrel s feet in diameter of weight w lb is floating ...
 1.3.19: After a mass m is attached to a spring, it stretches it s units and...
 1.3.20: In 19, what is a differential equation for the displacement x(t) if...
 1.3.21: By Newtons universal law of gravitation the freefall acceleration ...
 1.3.22: Suppose a hole is drilled through the center of the Earth and a bow...
 1.3.23: Learning Theory In the theory of learning, the rate at which a subj...
 1.3.24: Forgetfulness In assume that the rate at which material is forgotte...
 1.3.25: Infusion of a Drug A drug is infused into a patients bloodstream at...
 1.3.26: Tractrix A person P, starting at the origin, moves in the direction...
 1.3.27: Reflecting Surface Assume that when the plane curve C shown in Figu...
 1.3.28: Reread in Exercises 1.1 and then give an explicit solution P(t) for...
 1.3.29: Reread the sentence following equation (3) and assume that Tm is a ...
 1.3.30: Reread the discussion leading up to equation (8). If we assume that...
 1.3.31: Population Model The differential equation where k is a positive co...
 1.3.32: Rotating Fluid As shown in Figure 1.3.22(a), a rightcircular cylind...
 1.3.33: Falling Body In 21, suppose r R s, where s is the distance from the...
 1.3.34: Raindrops Keep Falling In meteorology the term virga refers to fall...
 1.3.35: Let It Snow The snowplow problem is a classic and appears in many d...
 1.3.36: Find the text Differential Equations, Ralph Palmer Agnew, McGrawHi...
Solutions for Chapter 1.3: Differential Equations as Mathematical Models
Full solutions for Differential Equations with BoundaryValue Problems  7th Edition
ISBN: 9780495108368
Solutions for Chapter 1.3: Differential Equations as Mathematical Models
Get Full SolutionsChapter 1.3: Differential Equations as Mathematical Models includes 36 full stepbystep solutions. This textbook survival guide was created for the textbook: Differential Equations with BoundaryValue Problems, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Differential Equations with BoundaryValue Problems was written by and is associated to the ISBN: 9780495108368. Since 36 problems in chapter 1.3: Differential Equations as Mathematical Models have been answered, more than 15501 students have viewed full stepbystep solutions from this chapter.

Arctangent function
See Inverse tangent function.

Bar chart
A rectangular graphical display of categorical data.

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.

Imaginary axis
See Complex plane.

Limaçon
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

Measure of center
A measure of the typical, middle, or average value for a data set

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

nth root of a complex number z
A complex number v such that vn = z

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Phase shift
See Sinusoid.

Polar axis
See Polar coordinate system.

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Sample space
Set of all possible outcomes of an experiment.

Stem
The initial digit or digits of a number in a stemplot.

Zero of a function
A value in the domain of a function that makes the function value zero.

Zoom out
A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).