Would you rather Put 3 dollars in the bank and have it triple each week for 4 weeks or put 4 dollars in the bank and have it quadruple each week for 3 weeks?

I'd rather use the second option that'd give me an amount of 256 by the end of the third week.

Step-by-step explanation:

In the first situation we have a initial amount of 3 dollars and it gets tripled every weeks for for weeks, so we have:

initial amount = 3

first week = 3*3 = 9

second week = 3*9 = 27

third week = 3*27 = 81

forth week = 3*81 = 243

In the second situation we have a initial amount of 4 dollars and get it quadruple each week for 3 weeks, so we have:

initial amount = 4

first week = 4*4 = 16

second week = 16*4 = 64

third week = 64*4 = 256

Another way of solving this is using geometric sequences. In these cases we have two sequences, the first one starts at 3 and a ratio of 3, while the second one starts at 4 and has a ratio of 4. We could use the formula for the nth term of a geometric seuqence that is:

a_n = a_1*[r^ (n-1) ]

On the first sequence we have a_1 = 3, r = 3 and n = 5 so we have:

a_5 = 3*[3^ (5-1) ] = 3*[3^4] = 3*81 = 243

On the second sequence we have a_1 = 4 r = 4 and n = 4 so we have:

a_4 = 4*[4^ (4-1) ] = 4*[4^3] = 4*64 = 256

I'd rather use the second option that'd give me an amount of 256 by the end of the third week.