yui makes a list of the balances in her savings account at the end of each month. she notices that each…

yui makes a list of the balances in her savings account at the end of each month. she notices that each months total is 5% greater than the previous months total. she writes a recursive formula to describe the account balances. which value should she use as the common ratio? 0.05 0.5 1.05 5.0

yui makes a list of the balances in her savings account at the end of each month. she notices that each months total is 5% greater than the previous months total. she writes a recursive formula to describe the account balances. which value should she use as the common ratio? 0.05 0.5 1.05 5.0

Answer

Explanation:

Step1: Convert percentage to decimal

If a value is 5% greater than the previous one, we add 5% of the previous - value to the previous - value. 5% in decimal form is 0.05. Let the previous - month's balance be $x$. The current - month's balance $y$ is $y=x + 0.05x=(1 + 0.05)x=1.05x$.

Step2: Identify the common ratio

In a geometric - sequence (which is what the account balances form since there is a constant ratio between consecutive terms), the common ratio $r$ is the factor by which each term is multiplied to get the next term. Here, since the current - month's balance is 1.05 times the previous - month's balance, the common ratio $r = 1.05$.

Answer:

1.05