Question

Aditya deposits $500 in a savings account over the course of a year. He deposits money into the account throughout the next year until his balance is quadrupled. The next year he does the same and deposits money into the account until his previous year’s balance is quadrupled. Assume that this trend continues and his account does not earn interest. Consider his initial balance to be year one. What explicit formula can be used to determine the balance of his savings account at the end of n years?
an=4⋅500^n

an=500⋅4^n−1

an=500⋅4^n

an=4⋅500^n−1

I think its either B or C

Answer 1

This is the concept of sequences and series; we are required to obtain the formula that will model balance in Aditya savings account after n period of years.
Since the money invested every year after it quadruples. Here we shall use the exponential growth formula given by:
an=ba^x
where
b=initial amount=500
x=n=variable=time
a=4
Therefore our formula will be given by:
an=500(4)^n