It depends which portion of human achievement you're measuring. As a whole, we went straight from an industrial revolution to a technology revolution. Many look at the time frame from 200k years ago or so and now, and sure enough it is exponential, and human lifespan has fallen into that.

However human's are young when one's measuring progress on a Universal scale.

It is not beyond comprehension to imagine that our entire history thus far is a spike in sort of a nyse of some publically traded commodity - to do a human example which however complex tends to follow nature thus far... not that we're publically traded, just that our math follows the Universe.

When one looks not at the whole, but individual advancements; when was the last time we made a major leap in agriculture? Are we still building with brick and mortar? How much has the engine of the car really changed?

The problem is proponents look at human life in the scope of human advancement as a whole. As a whole, we have been exponentially advancing.

Life though is not a whole, it is a single thing - like brick and mortor or the engine of a car.

Now, you may argue about the engine of a car. I will say though despite the advances, they don't break the speed of sound much less the speed of light. If they were exponential they would break both by now.

The sum of human advancement in the short may be exponential. Individual items we've created advance exponentially, then exponentially slow in advancement. This is a bell curve.