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For my birthday my dad recently bought me a baby RES that is 1.5 in. (he did not know it was illegal). I did the research and currently have everything that my turtle needs. I currently keep it in a 30 gallon tank with a lamp, basking area and the works. The tank is 24x24x12 and filled about 60% to the top with water. I would like to know how fast my baby turtle will grow because I am aware of the 10 gallon per inch rule and my dad says I'm not getting a new tank in a while. If someone could please tell me how quickly he will outgrow his tank, I would greatly appreciate it

Well, ideal environment and average turtle will be about 4" at 1 year old.

You don't really "have to" follow the 10 gallons per inch rule. It's ideal, but won't
really affect your turtle negatively if not. Assuming you have enough water, UVB,
food, etc that is...

That's my humble opinion. I know aquarium is expensive. Or, you can try your
luck browsing craigslist.com.

Thanks for the info.
Also, will they will grow gradually over time
or will they have random spurts of rapid growth?

Like Kemul said, at 1 year old, an average is about 4" (but it will vary with genetics, feeding, etc.).
After that, RES tend to grow about 1" per year until they reach their biggest size.
The 30 gallon should be good for about a year, and you can stretch it for longer if you need to.

I would recommend saving your money, so you can help purchase the next tank you need. Keep an eye on craigslist and local classifieds, because good deals sometimes come up. Someone else who lives in California was saying that there are tons of great deals on craigslist for used aquariums.