# Thread: which function describes this change

1. ## which function describes this change

hello

an amount x is reduced by half for 3 times, from example x becomes x/2 and then x/2/2 (=x/4) and then x/4/2 (= x/8)

after that it is increased by x (so it becomes x/8 + x) and it is reduced by half for 3 times (9x/16, 9x/32, 9x/64)

and so on

is there an equation/function that can help me calculate the amount of x after 1095 reduction times (taking into account the increase that occurs every 3rd reduction)

thanks

2. Originally Posted by mathos
hello

an amount x is reduced by half for 3 times, from example x becomes x/2 and then x/2/2 (=x/4) and then x/4/2 (= x/8)

after that it is increased by x (so it becomes x/8 + x) and it is reduced by half for 3 times (9x/16, 9x/32, 9x/64)

and so on

is there an equation/function that can help me calculate the amount of x after 1095 reduction times (taking into account the increase that occurs every 3rd reduction)

thanks
So, after 3 times it is x/8+x= x/8+ 8x/8= 9x/8 and then repeats: (9x/8)/8+ (9x/8)= 9x/64+ 9x/8= 9x/64+ 72x/64= 81x/64= $(9/8)^2x$. And then repeats again: (81x/64)/8+ (81x/64)= 81x/512+ 81x/64= 81x/512+ 648x/512= 729x/512= $(9/8)^3x$. Looks to me like, after 3n "reduction times" x is multiplied by $(9/8)^n$.

Now 1095/3= 365 so 1095= 3(365).