Question
An investor deposited money into an investment account that earns interest compounded annually. The function shown models the amount of money in the account in dollars after & years.
A(г) = 1,550(1.02)'
Which statement best interprets one value of the function?
• The initial deposit in the investment account was $1,581.
• The amount of money in the investment account increases
102% each year.
• The initial deposit in the investment account was $1,550.
• The amount of money in the investment account decreases 2% each year.
A(г) = 1,550(1.02)'
Which statement best interprets one value of the function?
• The initial deposit in the investment account was $1,581.
• The amount of money in the investment account increases
102% each year.
• The initial deposit in the investment account was $1,550.
• The amount of money in the investment account decreases 2% each year.
Answers
GPT-4o mini
To interpret the function \( A(t) = 1,550(1.02)^t \), we can analyze it as follows:
- The value \( 1,550 \) represents the initial deposit made into the investment account.
- The term \( (1.02)^t \) indicates that the amount increases by a factor of 1.02 each year, which corresponds to a 2% increase annually.
Now, let's evaluate the statements provided:
1. **The initial deposit in the investment account was $1,581.**
- This is incorrect because the initial deposit is $1,550, not $1,581.
2. **The amount of money in the investment account increases 102% each year.**
- This is incorrect because an increase of 102% implies that the account value would more than double, instead it increases by 2% each year.
3. **The initial deposit in the investment account was $1,550.**
- This is correct as it directly reflects the value of the initial deposit in the function.
4. **The amount of money in the investment account decreases 2% each year.**
- This is incorrect; the investment actually grows by 2% each year, not decreases.
Given this analysis, the statement that best interprets one value of the function is:
**The initial deposit in the investment account was $1,550.**
- The value \( 1,550 \) represents the initial deposit made into the investment account.
- The term \( (1.02)^t \) indicates that the amount increases by a factor of 1.02 each year, which corresponds to a 2% increase annually.
Now, let's evaluate the statements provided:
1. **The initial deposit in the investment account was $1,581.**
- This is incorrect because the initial deposit is $1,550, not $1,581.
2. **The amount of money in the investment account increases 102% each year.**
- This is incorrect because an increase of 102% implies that the account value would more than double, instead it increases by 2% each year.
3. **The initial deposit in the investment account was $1,550.**
- This is correct as it directly reflects the value of the initial deposit in the function.
4. **The amount of money in the investment account decreases 2% each year.**
- This is incorrect; the investment actually grows by 2% each year, not decreases.
Given this analysis, the statement that best interprets one value of the function is:
**The initial deposit in the investment account was $1,550.**