Which of the following savings account plans would yield exponential growth of the money in the account?
Choose 1 answer:
Choose 1 answer:
(Choice A)   
\[2\%\] of the initial value of the account is added to the value of the account each year.
A
\[2\%\] of the initial value of the account is added to the value of the account each year.
(Choice B, Checked)   
\[1.5\%\] of the current value of the account is added to the value of the account each year.
B
\[1.5\%\] of the current value of the account is added to the value of the account each year.
(Choice C)   A 
\[\$500\] signing bonus is added when the account is first opened, and 
\[0.5\%\] of the initial value of the account is added to the value of the account each year.
C
A 
\[\$500\] signing bonus is added when the account is first opened, and 
\[0.5\%\] of the initial value of the account is added to the value of the account each year.
(Choice D)   A 
\[\$100\] customer loyalty bonus is added to the account each year.
D
A 
\[\$100\] customer loyalty bonus is added to the account each year.

The correct answer is **Choice B: 1.5% of the current value of the account is added to the value of the account each year**.

Explanation:
- Exponential growth occurs when a quantity increases by a fixed percentage of its current value over time. In this case, Choice B describes such a scenario because each year, 1.5% of the **current value** of the account is added, which means the growth rate depends on the size of the account at that time. This is characteristic of exponential growth.

- The other options do not describe exponential growth:
  - **Choice A** adds a fixed percentage of the initial value each year, which is linear growth.
  - **Choice C** adds a one-time bonus and a fixed percentage of the initial value, which is also linear.
  - **Choice D** adds a fixed amount each year, which is another example of linear growth.

Do you want more details or have any questions?

Here are 5 related questions to explore:
1. What is the formula for calculating exponential growth in savings accounts?
2. How does compound interest differ from simple interest?
3. Can you explain the difference between linear and exponential growth in financial terms?
4. How does the rate of growth affect the total savings in the long term?
5. What is the impact of compounding frequency (e.g., annually, monthly) on exponential growth?

**Tip:** Exponential growth benefits more from a percentage of a growing total, meaning the larger the current value, the larger the increase each time!

Which of the following savings account plans would yield exponential growth of the money in the account? (Choice B) 1.5% of the current value of the account is added to the value of the account each year.

Learn how savings accounts with 1.5% of the current value added each year lead to exponential growth. Explore key concepts such as exponential growth, percentage increase, and how financial mathematics applies to savings plans. Suitable for students in Grades 9-12.

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