1 Nov 2021
Problem 15c
Page 499
Section 7.1: Modeling with Differential Equations
Chapter 7: Differential Equations
Textbook ExpertVerified Tutor
1 Nov 2021
Given information
As per the given question ,
- The derivative represents the rate at which performance improves.
Step-by-step explanation
Step 1.
If
Geometrically, when we impose an initial condition, we look at the family of solution curves and pick the one that passes through the point
From part (b) the differential equation is
is a positive constant
Referring to the earlier solutions,
Performance increases most rapidly initially, and decreases as increases and when approaching then approaches zero
Let be the equilibrium that is the maximum level of performance of which the learner is capable
Therefore, if we try to draw the graph of over then graph is increasing and after some time the rate of increase is decreases and it approaches zero near equilibrium
Plot the axis and axis and plot the graph as shown in figure,