If the data appear to be exponential, what non-linear transformation might be appropriate for linearizing the data?
You use the logarithm function.
With logarithms (log) you reduce a multiplication (a growth factor) to an addition. E.g. every time you multiply by 2, the log goes up approx. 0.3. So a formula like 2^t becomes 0.3t, and that's a straight line.
You can do this in several ways: In the old days we used log-graph-paper. Also programs like Excel can let you plot logarithmically.
I always use the following example: the smallest sound you can hear is one tree leaf moving in a very soft breeze. For a sound to hurt your ears you will need 10000000000000 times as much, with everything in between. What if we just write down the size of the number in stead of the number itself? So the one leaf (no zeroes) we write down as 0 and the greater number as 13 (zeroes). That's logarithms.