Percent of percent chain

Question

Start out with a number, for example 458.

The number is reduced by 1% 35 times, so:

• 458
• 453.42
• 448.89
• ...
• 322.18

How can I calculate final number without doing a step-wise reduction?

Answer 1

Hint: If you multiply $x$ by $a$, the result is $$ xa $$ If you again multiply it by $a$, the result becomes $$ xa^2 $$ If you again multiply it by $a$, the result becomes $$ xa^3 $$ Can you see the pattern?