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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?

Respuesta :

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

[tex]81\times(3)^3[/tex]

Since

[tex]81=3^4[/tex]

the above can be written as

[tex]3^4\times3^3[/tex]

Using the property of the exponents that

[tex]a^x\times a^y=a^{x+y}[/tex]

we rewrite the above as

[tex]3^4\times3^3=3^{4+3}=\textcolor{#FF7968}{3^7}\text{\textcolor{#FF7968}{.}}[/tex]

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

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