Yes yes, we all know that exponential growth is pretty cool. But take into account that you can't explode outwards in the Martian environment like some algae growing in a food rich environment, every new person and every piece of infrastructure will need (a lot of) maintenance and that slows down doubling rate by a lot. You also can't use a lot of Earth-based shortcuts either, since there is no oxygen for fossil fuels and you won't be able to grow food in open atmosphere.

Big industrial equipment is really heavy btw, so you could fit at most 1 or 2 pieces of big equipment in the 100 ton payload of a Starship rocket. It could easily be a few hundred launches just to get a proper scale foundry going on mars, if you take into account all the required auxiliary equipment like ore scrubbers, cranes and forklifts. Don't forget all the solar panels and/or nuclear plants for power generation too. It would probably be at least tens of billions of support from Earth.

All in all, I would think that 5-10% growth rate is already pretty ambitious, leading to a doubling rate of 7 to 14 years. If you start your colony with about 50 people, it would rise to a thousand people in a little over 50 years.