Alison deposits into a new savings account that earns
percent interest compounded annually. If Alison makes no additional deposits or withdrawals, how many years will it take for the amount in the account to double?
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After year, the amount in the account is equal to
. After
years, the amount is equal to
, and so on. After
years, the amount is equal to
. You need to find the value of
for which
. There are several ways to solve this equation. You can use logarithms to solve the equation as follows.

Since , it will take more than
years for the amount in the account to double. Thus, you need to round
up to
.
Another way to find is to use your graphing calculator to graph
and
. From the answer choices, you know you need to set the viewing window with
values from
to about
and
values extending just beyond
. The
of the point of intersection is approximately
. Thus you need to round up to
.