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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,
 

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 
3) Calculation:
From part (b) the differential equation is
 is a positive constant
By our earlier discussion,
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,

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