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 .