Determine which of the following scenarios could be modeled by an arithmetic sequence. (Could be more than one answer) (4 points)
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.
You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter.
You keep your money in a savings account that pays you 10% interest each week.
The scenario that could be modeled by an arithmetic sequence is:
- You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter.
The first scenario, where a cane of bamboo grows 6 inches per week, can be modeled by an arithmetic sequence.
To determine which of the scenarios could be modeled by an arithmetic sequence, we need to understand what an arithmetic sequence is.
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant.
Let's analyze each scenario:
1. A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter.
In this scenario, the height of the bamboo grows by a constant value of 6 inches every week. Hence, this scenario 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 magic penny doubles every day. The rate of growth is not constant because it doubles rather than incrementing by a constant value. Therefore, this scenario 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.
In this scenario, the amount borrowed decreases by a constant value of $25 each week. Since the difference between the terms is constant, this scenario 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 is a percentage, not a constant value. As the interest is calculated based on the amount in the savings account each week, the growth rate is not constant. Hence, this scenario cannot be modeled by an arithmetic sequence.
Based on the analysis above, the scenarios that can 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.
3. You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter.