a.
To write a recursive definition and an explicit formula for the amount of money at the end of any week.
The recursive definition is
Given information:
Bank offers to start a saving account depositing $25 and depositing $5 a week starting the next week.
Calculation:
The initial amount is $25. So,
The amount at the end of second, third and fourth week will be:
So, the recursive definition can be written as
The values of the amounts at the end of the first four week will be:
This represents an arithmetic sequence with
b.
To find the amount in the bank after 4 weeks.
The amount in the bank at the end of the 4th week will be $40.
Given information:
Bank offers to start a saving account depositing $25 and depositing $5 a week starting the next week.
Calculation:
From part (a), the amount at the end of any week can be obtained using the formula,
Substitute
Therefore, the amount in the bank at the end of the 4th week will be $40.
c.
To write the recursive formula for the amount of money after every interest payment.
The recursive formula for the amount after every interest paid is
Given information:
Bank offers to start a saving account depositing $25 and depositing $5 a week starting the next week.
Calculation:
The recursive formula from part (a) is
The recursive formula for the amount at the end of every four week can be given as
After the interest payment the amount will be:
Therefore, the recursive formula for the amount after every interest paid is
d.
To find the bank’s annual interest rate.
The annual interest rate of the bank is
Given information:
Bank offers to start a saving account depositing $25 and depositing $5 a week starting the next week.
Calculation:
Since the amount at every four week is multiplied by
Multiply this by 12 to get the annual interest rate of the bank.
So, the annual interest rate of the bank is
Chapter 9 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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