Hi all, please help me to solve this using Law of Indices

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Winifred909

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If one dollar is placed into an account triples every 12 years, how much will it be in the account after 60 years?
 
12 divides into 60 5 times so there are 5 periods of 12 years in 60 years. After the first 12 years, $1 will triple to become 3*1= $3. After the second, 3*3= $9. After the third, 3*9= $27. After the fourth, 3*27= $81. And after the fifth, 3*81= $243. There will be $243 in the account after 60 years.

Of course, that is more easily written \(\displaystyle 3^5= $243\).
 
I'm going to invest $1 into this account today. Boy will I be rich in 60 years (and extremely old!)
 
HallsofIvy said:
12 divides into 60 5 times so there are 5 periods of 12 years in 60 years. After the first 12 years, $1 will triple to become 3*1= $3. After the second, 3*3= $9. After the third, 3*9= $27. After the fourth, 3*27= $81. And after the fifth, 3*81= $243. There will be $243 in the account after 60 years.

Of course, that is more easily written \(\displaystyle 3^5= $243\).
Click to expand...
Thanks,
 
Please define "Law of Indices". Is it a thing? A collection of things? A set of rules or a single rule?

If r is an vaguely-defined accumulation factor, we have:

$1 * r * r * r * ... * r (60 multiplications by r)
= $1 * (r * r * r * ... * r) * (r * r * r * ... * r) * (r * r * r * ... * r) * (r * r * r * ... * r) * (r * r * r * ... * r) (60 multiplications by r in 5 groups of 12)
= $1 * r^12 * r^12 * r^12 * r^12 * r^12
= $1 * 3 * 3 * 3 * 3 * 3
= $1 * 3^5

Did I use the "Law of Indices" or not?
 
Winifred909 said:
Based on Hallsofly's explanation, could it be summarized as 3^1 x 3^4 = $243
Click to expand...
I think you'll have to decide on your own conditions for satisfying the odd request to demonstrate the "Law of Indices".
 
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