To be fair, exponential growth can have a rather large time-constant and it still is exponential. Most valuation/inflation/stock market/house market plots that span more than a decade or two are indeed logarithmic plots because much of these curves indeed follow exponentials.

To be also fair, exponential growth basically does not exist in nature; if you think you have exponential growth, you actually have truncated logistic growth.

Exponential growth is not necessarily fast growth. If r is .00000001 and the period is one year, then the curve would look flat on any human timescale.