- 3.1: If P(t) P0e0.15t gives the population in an environment at time t, ...
- 3.2: If the rate of decay of a radioactive substance is proportional to ...
- 3.3: In March 1976 the world population reached 4 billion. At that time,...
- 3.4: Air containing 0.06% carbon dioxide is pumped into a room whose vol...
- 3.5: Solve the differential equation of the tractrix. See in Exercises 1...
- 3.6: Suppose a cell is suspended in a solution containing a solute of co...
- 3.7: Suppose that as a body cools, the temperature of the surrounding me...
- 3.8: According to Stefans law of radiation the absolute temperature T of...
- 3.9: An LR series circuit has a variable inductor with the inductance de...
- 3.10: A classical problem in the calculus of variations is to find the sh...
- 3.11: A model for the populations of two interacting species of animals i...
- 3.12: Initially, two large tanks A and B each hold 100 gallons of brine. ...
- 3.13: When all the curves in a family G(x, y, c1) 0 intersect orthogonall...
- 3.14: When all the curves in a family G(x, y, c1) 0 intersect orthogonall...
- 3.15: Aquifers and Darcys Law According to the Sacramento, California, De...
- 3.16: Population Growth Models We can use direction fields to obtain a gr...
Solutions for Chapter 3: MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS
Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition
artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in three-dimensional space and ordered triples of real numbers
Axis of symmetry
See Line of symmetry.
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once
A set of points in a plane equally distant from a fixed point called the center
Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data
See Compounded k times per year.
Explicitly defined sequence
A sequence in which the kth term is given as a function of k.
Points that satisfy the constraints in a linear programming problem.
The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.
Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).
The diagonal from the top left to the bottom right of a square matrix
The value of |r| at the point on the graph of a polar equation that has the maximum distance from the pole
Measure of an angle
The number of degrees or radians in an angle
Projection of u onto v
The vector projv u = au # vƒvƒb2v
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series
p = ƒ(x), where x represents production and p represents price
A function that maps real numbers to real numbers.
The scale of the tick marks on the y-axis in a viewing window.