You are not planning to go into a math related discipline, I hope ;-)

"Doubling every year" is this function: 2^x, where x is the number of years that have passed.

It is true that in the case of car ownership, the growth has an upper bound and the doubling must level off, but that doesn't preclude a period of time where change is exponential.

I'm guessing you are thinking of curves that have an asymptope, and therefore a boundary value for the function. But a logarithm does not guarantee you an upper bound.

Consider the function y = ln(x). Can you find an upper bound ?

Likewise, power functions can be bounded. (1/x)^n looking at n from 0 to infinity has asymptopes easily discernible.

Logs and exponents are inverse functions of each other. They are both curves. And, though I am not a mathematician, I am reasonably sure they have similar characteristics.