How many days would it take for a crepe myrtle tree to grow 1 cm in height if it grows 3.38 feet per year?

It's very easy, it's depending mainly on converting a mathematical unit:

When 1 Cm = 0.0328084 Ft

So, we assume that:

in 1 year → it grows 3.38 Ft

So X (years) → 0.0328084

∴X (years) = 0.0328084 * 3.38 = 0.0097 year

We have to convert this unit form years to days by:

1 year = 365 days

So, 0.0097 = X (days)

∴X (days) = 365 * 0.0097 = 3.5 days

So it will take 3.5 days to grow up