Doubling the genome in a single generation keeps the functional genome the same size. The copies need to mutate so that they can be assigned to new jobs.
The genes are useful to only their already existing jobs. They become useful to new jobs as time passes. Time can only modify the genes you already have, so the rate of evolution is proportional to the size of the genome already present, hence the exponential.
No species creates a completely a random chunk of DNA 100 times the size of its current DNA, waits it to mutate and checks once in a while if any segment of it can be used in a useful way. They don’t build up usefulness from scratch.
Why faster back then? The observed pattern is that evolution has a constant exponential speed and life must be 10 billion years old (the times when it hibernated or remained dead doesn’t count)
It doesn’t become functional when you double it. It doesn’t take new functions.
We can write a formula for the speed of evolution in the following way:
E = C x M
The speed of evolution is equal to the speed of copying times the speed of modifying. Copying refers to when you double your genes one by one or the whole genome at the same time. Modifying refers to turning those non functional copies into functional ones. What causes copying is mutations, and what causes modifying is mutations and natural selection.
The speed of copying is proportional to your genome size, because if you have a large genome, you would have more genes to copy.
Life goes from less complexity to more complexity, because if you have only a few genes, the information they are coding can’t be that much. And genome sizes have been increasing. What I referred to as “the speed of evolution” in the formula above is the speed of the increase in complexity. If you kept the same genome size, and only changed what it coded for, it would still be evolution, but it wouldn’t be “progress”
When you are copying your genome, the copying you can make is proportional to the genome size you already have. So after some time passes, a small genome would have grown by a small amount, and a large genome can grow by a large amount. Which function’s derivative is equal to itself? Its the exponential function.
The complexification or progress can stop when new progress is no longer needed. But the fact that life needs 10 billion years to get to where it is right now suggest that life on earth has to be 10 billion years old or older.