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.
In this scenario, the amount borrowed decreases by a constant value of $25 each week, forming an arithmetic sequence.
The scenarios that could be modeled by an arithmetic sequence are:
1. 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 fixed amount of $25 each week. This constant decrease forms an arithmetic sequence.
2. You keep your money in a savings account that pays you 10% interest each week.
In this scenario, the amount of interest earned each week is a fixed percentage of the initial amount. Since the interest is calculated based on a fixed rate, it forms an arithmetic sequence.
So, the correct answers are options 3 and 4.
To determine which of the scenarios could be modeled by an arithmetic sequence, we need to analyze the given information for each scenario.
1. In the first scenario, a cane of bamboo starts at 30 inches tall and grows by 6 inches per week. This does not represent an arithmetic sequence because the growth rate is not constant.
2. In the second scenario, a magic penny doubles in value every day for 30 days. Since the value doubles every day, this does not represent an arithmetic sequence either because the growth rate is not constant.
3. In the third scenario, you borrow $350 from a friend the first week and pay the friend back $25 each week thereafter. This represents an arithmetic sequence. The initial amount borrowed is $350, and each subsequent payment decreases by $25, indicating a constant payment rate.
4. In the fourth scenario, you keep your money in a savings account that pays you 10% interest each week. As the interest is given as a percentage, the growth rate is not constant, and therefore this does not represent an arithmetic sequence.
Based on the analysis, only the third scenario, where you borrow $350 from a friend and pay back $25 each week thereafter, can be modeled by an arithmetic sequence.