Explanation Given information: If y ( 0 ) = 100 and y ′ = 0.2 y then y ( 1 ) ≈ 20 . Assume the rate of growth is approximately constant over unit intervals. Calculation: We have y ′ = 0.2 y Solving the differential equation, we get y = e 0.2 x + c Substitute y ( 0 ) = 100 to find value of c. 100 = e 0

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 9, Problem 17SYU

To determine

Indicate whether the statement is true of false.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 16SYU

Chapter 9, Problem 18SYU

Students have asked these similar questions

Explain the key points and reasons for 12.8.2 (1) and 12.8.2 (2)

Q1: A slider in a machine moves along a fixed straight rod. Its distance x cm along the rod is given below for various values of the time. Find the velocity and acceleration of the slider when t = 0.3 seconds. t(seconds) x(cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 30.13 31.62 32.87 33.64 33.95 33.81 33.24 Q2: Using the Runge-Kutta method of fourth order, solve for y atr = 1.2, From dy_2xy +et = dx x²+xc* Take h=0.2. given x = 1, y = 0 Q3:Approximate the solution of the following equation using finite difference method. ly -(1-y= y = x), y(1) = 2 and y(3) = −1 On the interval (1≤x≤3).(taking h=0.5).

Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

Chapter 9 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

Ch. 9.1 - Prob. 1P Ch. 9.1 - Prob. 2P Ch. 9.1 - Prob. 3P Ch. 9.1 - Prob. 4P Ch. 9.1 - Prob. 5P Ch. 9.1 - Prob. 6P Ch. 9.1 - Prob. 7P Ch. 9.1 - Prob. 8P Ch. 9.1 - Prob. 9P Ch. 9.1 - Prob. 10P

Ch. 9.1 - Prob. 11P Ch. 9.1 - Prob. 12P Ch. 9.1 - Prob. 13P Ch. 9.1 - Prob. 14P Ch. 9.1 - Prob. 15P Ch. 9.1 - Prob. 16P Ch. 9.2 - Prob. 1P Ch. 9.2 - Prob. 2P Ch. 9.2 - Prob. 3P Ch. 9.2 - Prob. 4P Ch. 9.2 - Prob. 5P Ch. 9.2 - Prob. 6P Ch. 9.2 - Prob. 7P Ch. 9.2 - Prob. 8P Ch. 9.2 - Prob. 9P Ch. 9.2 - Prob. 10P Ch. 9.2 - Prob. 11P Ch. 9.2 - Prob. 12P Ch. 9.2 - Prob. 13P Ch. 9.2 - Prob. 14P Ch. 9.2 - Prob. 15P Ch. 9.2 - Prob. 16P Ch. 9.2 - Prob. 17P Ch. 9.2 - Prob. 18P Ch. 9.2 - Prob. 19P Ch. 9.2 - Prob. 20P Ch. 9.2 - Prob. 21P Ch. 9.2 - Prob. 22P Ch. 9.3 - Prob. 1P Ch. 9.3 - Prob. 2P Ch. 9.3 - Prob. 3P Ch. 9.3 - Prob. 4P Ch. 9.3 - Prob. 5P Ch. 9.3 - Prob. 6P Ch. 9.3 - Prob. 7P Ch. 9.3 - Prob. 8P Ch. 9.3 - Prob. 9P Ch. 9.3 - Prob. 10P Ch. 9.3 - Prob. 11P Ch. 9.3 - Prob. 12P Ch. 9.3 - Prob. 13P Ch. 9.3 - Prob. 14P Ch. 9.3 - Prob. 15P Ch. 9.3 - Prob. 16P Ch. 9.3 - Prob. 17P Ch. 9.4 - Prob. 1P Ch. 9.4 - Prob. 2P Ch. 9.4 - Prob. 3P Ch. 9.4 - Prob. 4P Ch. 9.4 - Prob. 5P Ch. 9.4 - Prob. 6P Ch. 9.4 - Prob. 7P Ch. 9.4 - Prob. 8P Ch. 9.4 - Prob. 9P Ch. 9.4 - Prob. 10P Ch. 9.4 - Prob. 11P Ch. 9.4 - Prob. 12P Ch. 9.4 - Prob. 13P Ch. 9.4 - Prob. 14P Ch. 9.4 - Prob. 15P Ch. 9.4 - Prob. 16P Ch. 9.4 - Prob. 17P Ch. 9.5 - Prob. 1P Ch. 9.5 - Prob. 2P Ch. 9.5 - Prob. 3P Ch. 9.5 - Prob. 4P Ch. 9.5 - Prob. 5P Ch. 9.5 - Prob. 6P Ch. 9.5 - Prob. 7P Ch. 9.5 - Prob. 8P Ch. 9.5 - Prob. 9P Ch. 9.5 - Prob. 10P Ch. 9.5 - Prob. 11P Ch. 9.5 - Prob. 12P Ch. 9.5 - Prob. 13P Ch. 9.5 - Prob. 14P Ch. 9.5 - Prob. 15P Ch. 9.5 - Prob. 16P Ch. 9.5 - Prob. 17P Ch. 9.5 - Prob. 18P Ch. 9.5 - Prob. 19P Ch. 9.5 - Prob. 20P Ch. 9.5 - Prob. 21P Ch. 9.5 - Prob. 22P Ch. 9.5 - Prob. 23P Ch. 9.5 - Prob. 24P Ch. 9.5 - Prob. 25P Ch. 9.6 - Prob. 1P Ch. 9.6 - Prob. 2P Ch. 9.6 - Prob. 3P Ch. 9.6 - Prob. 4P Ch. 9.6 - Prob. 5P Ch. 9.6 - Prob. 6P Ch. 9.6 - Prob. 7P Ch. 9.6 - Prob. 8P Ch. 9.6 - Prob. 9P Ch. 9.6 - Prob. 10P Ch. 9.6 - Prob. 11P Ch. 9.6 - Prob. 12P Ch. 9.6 - Prob. 13P Ch. 9.6 - Prob. 14P Ch. 9.6 - Prob. 15P Ch. 9.6 - Prob. 16P Ch. 9.6 - Prob. 17P Ch. 9.6 - Prob. 18P Ch. 9.6 - Prob. 19P Ch. 9.6 - Prob. 20P Ch. 9.6 - Prob. 21P Ch. 9.6 - Prob. 22P Ch. 9.6 - Prob. 23P Ch. 9.6 - Prob. 24P Ch. 9.6 - Prob. 25P Ch. 9.6 - Prob. 26P Ch. 9.7 - Prob. 1P Ch. 9.7 - Prob. 2P Ch. 9.7 - Prob. 3P Ch. 9.7 - Prob. 4P Ch. 9.7 - Prob. 5P Ch. 9.7 - Prob. 6P Ch. 9.7 - Prob. 7P Ch. 9.7 - Prob. 8P Ch. 9.7 - Prob. 9P Ch. 9.7 - Prob. 10P Ch. 9.7 - Prob. 11P Ch. 9.7 - Prob. 12P Ch. 9 - Prob. 1SYU Ch. 9 - Prob. 2SYU Ch. 9 - Prob. 3SYU Ch. 9 - Prob. 4SYU Ch. 9 - Prob. 5SYU Ch. 9 - Prob. 6SYU Ch. 9 - Prob. 7SYU Ch. 9 - Prob. 8SYU Ch. 9 - Prob. 9SYU Ch. 9 - Prob. 10SYU Ch. 9 - Prob. 11SYU Ch. 9 - Prob. 12SYU Ch. 9 - Prob. 13SYU Ch. 9 - Prob. 14SYU Ch. 9 - Prob. 15SYU Ch. 9 - Prob. 16SYU Ch. 9 - Prob. 17SYU Ch. 9 - Prob. 18SYU Ch. 9 - Prob. 19SYU Ch. 9 - Prob. 20SYU Ch. 9 - Prob. 21SYU Ch. 9 - Prob. 22SYU Ch. 9 - Prob. 23SYU Ch. 9 - Prob. 24SYU Ch. 9 - Prob. 25SYU Ch. 9 - Prob. 26SYU Ch. 9 - Prob. 27SYU Ch. 9 - Prob. 28SYU Ch. 9 - Prob. 29SYU Ch. 9 - Prob. 30SYU Ch. 9 - Prob. 31SYU Ch. 9 - Prob. 32SYU Ch. 9 - Prob. 33SYU Ch. 9 - Prob. 34SYU Ch. 9 - Prob. 35SYU Ch. 9 - Prob. 36SYU Ch. 9 - Prob. 37SYU Ch. 9 - Prob. 38SYU Ch. 9 - Prob. 39SYU Ch. 9 - Prob. 40SYU Ch. 9 - Prob. 41SYU Ch. 9 - Prob. 42SYU Ch. 9 - Prob. 43SYU Ch. 9 - Prob. 44SYU Ch. 9 - Prob. 45SYU Ch. 9 - Prob. 46SYU Ch. 9 - Prob. 47SYU Ch. 9 - Prob. 48SYU Ch. 9 - Prob. 49SYU Ch. 9 - Prob. 50SYU Ch. 9 - Prob. 51SYU Ch. 9 - Prob. 52SYU Ch. 9 - Prob. 53SYU Ch. 9 - Prob. 54SYU Ch. 9 - Prob. 55SYU Ch. 9 - Prob. 56SYU Ch. 9 - Prob. 57SYU Ch. 9 - Prob. 58SYU Ch. 9 - Prob. 59SYU Ch. 9 - Prob. 60SYU Ch. 9 - Prob. 61SYU Ch. 9 - Prob. 62SYU Ch. 9 - Prob. 63SYU Ch. 9 - Prob. 64SYU Ch. 9 - Prob. 65SYU Ch. 9 - Prob. 66SYU Ch. 9 - Prob. 67SYU Ch. 9 - Prob. 68SYU Ch. 9 - Prob. 69SYU Ch. 9 - Prob. 70SYU Ch. 9 - Prob. 1FOT Ch. 9 - Prob. 2FOT Ch. 9 - Prob. 3FOT Ch. 9 - Prob. 4FOT Ch. 9 - Prob. 5FOT Ch. 9 - Prob. 6FOT Ch. 9 - Prob. 7FOT Ch. 9 - Prob. 8FOT Ch. 9 - Prob. 9FOT Ch. 9 - Prob. 10FOT Ch. 9 - Prob. 11FOT Ch. 9 - Prob. 12FOT Ch. 9 - Prob. 13FOT Ch. 9 - Prob. 14FOT Ch. 9 - Prob. 15FOT Ch. 9 - Prob. 16FOT Ch. 9 - Prob. 17FOT Ch. 9 - Prob. 18FOT Ch. 9 - Prob. 19FOT Ch. 9 - Prob. 20FOT Ch. 9 - Prob. 21FOT

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Indicate whether the statement is true of false.

Solution Summary: The author explains whether the statement is true or false. The rate of growth is approximately constant over unit intervals.

Concept explainers

Videos

Indicate whether the statement is true of false.

Want to see the full answer?

Chapter 9 Solutions