- 9.5.1: Find particular solutions in 18. dy dt = 0.5(y 200), y= 50 when t = 0
- 9.5.2: Find particular solutions in 18. dP dt = P + 4, P = 100 when t = 0
- 9.5.3: Find particular solutions in 18. dH dt = 3(H 75), H= 0 when t = 0
- 9.5.4: Find particular solutions in 18. dm dt = 0.1m + 200, m(0) = 1000
- 9.5.5: Find particular solutions in 18. dB dt = 4B 100, B= 20 when t = 0
- 9.5.6: Find particular solutions in 18. dQ dt = 0.3Q 120, Q= 50 when t = 0
- 9.5.7: Find particular solutions in 18. dB dt + 2B = 50, B(1) = 100
- 9.5.8: Find particular solutions in 18. dB dt + 0.1B 10 = 0 B(2) = 3
- 9.5.9: Check that y = A+Cekt is a solution to the differential equation dy...
- 9.5.10: A bank account earns 5% annual interest, compounded continuously. M...
- 9.5.11: Money in an account earns interest at a continuous rate of 8% per y...
- 9.5.12: A company earns 2% per month on its assets, paid continuously, and ...
- 9.5.13: A bank account earns 7% annual interest compounded continuously. Yo...
- 9.5.14: One theory on the speed an employee learns a new task claims that t...
- 9.5.15: A patient is given the drug theophylline intravenously at a rate of...
- 9.5.16: A chain smoker smokes five cigarettes every hour. From each cigaret...
- 9.5.17: As you know, when a course ends, students start to forget the mater...
- 9.5.18: (a) Find the equilibrium solution of the equation dy dt = 0.5y 250....
- 9.5.19: (a) What are the equilibrium solutions for the differential equatio...
- 9.5.20: Figure 9.38 gives the slope field for a differential equation. Esti...
- 9.5.21: A yam is put in a 200C oven and heats up according to the different...
- 9.5.22: At 1:00 pm one winter afternoon, there is a power failure at your h...
- 9.5.23: A detective finds a murder victim at 9 am. The temperature of the b...
- 9.5.24: A drug is administered intravenously at a constant rate of r mg/hou...
- 9.5.25: Some people write the solution of the initial value problem dy dt =...
Solutions for Chapter 9.5: APPLICATIONS AND MODELING
Full solutions for Applied Calculus | 5th Edition
Acceleration due to gravity
g ? 32 ft/sec2 ? 9.8 m/sec
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects
The central point in a circle, ellipse, hyperbola, or sphere
Equivalent systems of equations
Systems of equations that have the same solution.
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.
The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.
Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.
Initial side of an angle
Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth
Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial
Multiplicative identity for matrices
See Identity matrix
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.
One-to-one rule of exponents
x = y if and only if bx = by.
Product of complex numbers
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
Reflection across the x-axis
x, y and (x,-y) are reflections of each other across the x-axis.
See Division algorithm for polynomials.
The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.
A set of points in Cartesian space equally distant from a fixed point called the center.
An identity involving a trigonometric function of u + v
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