Does the 1 percent better every day exponential growth formula 1 point 01 to the power of 365 actually work

Theres this quote going around:

"If you get 1% better every day, after one year you'll be $1.01^{365} \approx 37.78$ times better!"

And the negative version: "If you get 1% worse every day, $0.99^{365} \approx 0.03$, so youre basically zero."

This sounds motivational but is it real math? Like can you compound self-improvement like compound interest?

Also, isnt $1.01^{365}$ a simplified calculation? Doesnt account for weekends or days you dont improve? If improvement only happens on weekdays (260 days), is it $1.01^{260} \approx 13$ times?

Whats the actual formula for skill growth over time according to educational psychology? Is it really exponential or more like logarithmic?