Exponential curves grow at the same rate all the time. That is, if you zoom in on the x^2 graph at any point at any scale, it will look exactly the same as it did before you zoomed in.
I think we are using “rate” in different ways. The absolute rate of change per unit time for an exponential is hardly constant; If you look at the segment of e^x near, say, e^10, it’s growing much faster than it is at e^(-10).
Err… minor quibble.
Exponential curves grow at the same rate all the time. That is, if you zoom in on the x^2 graph at any point at any scale, it will look exactly the same as it did before you zoomed in.
I think we are using “rate” in different ways. The absolute rate of change per unit time for an exponential is hardly constant; If you look at the segment of e^x near, say, e^10, it’s growing much faster than it is at e^(-10).