Just looking rough order of magnitude, you should start seeing exponential behavior when your expected investment gains (say 8% of portfolio values) are greater than your annual contribution - for most people about 10 years.

If you want a more mathematical answer, the exponential function is **very** well approximated by a line until a*t > 1 where a is the rate of return and t is the time. For an 8% market return, this works out to about 10 years. If you've taken calculus take a look at the Tayor expansion for e^(at) about the point t=0 and you'll see why this is true.

Also, there is a tremendous amount of noise in the stock market. In general, it takes at least 10 years, but often longer, to see clear trends in the data. Try using the index view tool MMM posted earlier this week with a 5 year window - you'll see many periods where a line fits the data just as well as an exponential. With a 30 year window, the exponential nature of growth is obvious.