It means that when you are writing the equation...the maximum power of x should be =1. For example y=x+5. This means that the increase is linear (and not exponential). Even y=2x+5 is considered as linear increase. Even y=100x+5 is considered a linear increase. y = 100x+5 will just have a more larger angle as compared to y=x+5.
Example of linear increase :- Increase in fans speed when you turn the regulator
But If there is any x2 or x3 term or so on....with higher powers of x, that means you are dealing with exponential powers of x (i.e exponential rates of growth)
Example of exponential increase : Bacterial increase
Plotting linear & exponential equations on an online graphing software to see contrast.
One way to find the difference between linear equations and exponential equations is to go to desmos.com or any other online graphing software and plot these equations.
It will look something like this
First, linear equations....
Now lets consider an exponential equation.
I want you to notice the lack of curves in the linear equation (y=x+70). Its just a straight line.
On the other hand, i want you to notice the present of curves in the exponential equation (y=x^2+7). Its a curved line. Can you imagine an equation having a x^2 term or a x^3 term not have any curve in it. In fact it is curved at every point, isn't it ?
This means that the double derivative (rate of change of rate of change) will be not equal to zero.
Rate of change/derivative = 0 means no change at w.r.t time. This will be a straight line running parallel to the x-axis.
Rate of change of Rate of change/ Derivative of Derivative =0 means there is a change w.r.t x axis, but this change is happening in a steady fixed slope manner.
Rate of change of Rate of change/ Derivative of Derivative = some value. This means that there is some curve in the slope (rate of change). This means rate of change is not fixed with time . It might be exponential w.r.t time
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