Respuesta :
Answer:
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.
