Question

Money that is collecting interest in a bank account triples in value every 20 years. When the account was opened, it had 81, or 3^4 dollars in it. After 60 years, the account balance has tripled 3 times, increasing by a factor of 33. It now has a balance of 3^4÷3^3. Expressed as a power, how much money, in dollars, is in the account after 60 years?

Answer 1

The money tripes every 20 years. There are 3 sets of 20 years in 60 years and the original amount was $81; therefore, after 60 the account balance will be

`81*(3)^3`

Since

`81=3^4`

the above can be written as

`3^4*3^3`

Using the property of the exponents that

`a^x* a^y=a^(x+y)`

we rewrite the above as

`3^4*3^3=3^(4+3)=\textcolor{#FF7968}{3^7}\text{\textcolor{#FF7968}{.}}`

Hence, after 60 years the account has 3^7 dollars.