Determine which of the following scenarios could be modeled by an arithmetic sequence. (Could be more than one answer)(4 points) Arithmetic Not Arithmetic A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter. Arithmetic – A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter. Not Arithmetic – A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter. You find a magic penny that doubles in value every day for 30 days. Arithmetic – You find a magic penny that doubles in value every day for 30 days. Not Arithmetic – You find a magic penny that doubles in value every day for 30 days. You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter. Arithmetic – You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter. Not Arithmetic – You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter. You keep your money in an savings account that pays you 10% interest each week.
Not Arithmetic – A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter.
Arithmetic – You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter.
The scenarios that could be modeled by an arithmetic sequence are:
1. A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter.
2. You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter.
To determine which scenarios can be modeled by an arithmetic sequence, we need to check if there is a consistent numerical pattern or common difference between the terms.
Let's analyze each scenario:
1. A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter.
- This scenario has a consistent numerical pattern since the height is increasing by 6 inches every week. Hence, it can be modeled by an arithmetic sequence.
2. You find a magic penny that doubles in value every day for 30 days.
- In this scenario, the value of the penny is doubling every day. Since the doubling factor is not constant (changing from 1 to 2), it does not have a consistent numerical pattern. Therefore, it cannot be modeled by an arithmetic sequence.
3. You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter.
- This scenario has a constant repayment amount of $25 every week. Hence, it has a consistent numerical pattern and can be modeled by an arithmetic sequence.
4. You keep your money in a savings account that pays you 10% interest each week.
- In this scenario, the interest rate of 10% per week would result in a compounding effect, not a consistent increase by a fixed amount. Therefore, it does not have a consistent numerical pattern and cannot be modeled by an arithmetic sequence.
In summary, the scenarios that can be modeled by an arithmetic sequence are:
- A cane of bamboo growing 6 inches per week
- Borrowing $350 and repaying $25 each week
The scenarios that cannot be modeled by an arithmetic sequence are:
- A magic penny doubling in value every day
- Earning 10% interest per week on savings account.