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 `t` years.`
A (t) =1,550 (1.02)^t
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 (t) =1,550 (1.02)^t
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
The function \( A(t) = 1,550 (1.02)^t \) represents the amount of money in the account after \( t \) years, where \( 1,550 \) is the initial deposit and \( 1.02 \) represents a growth factor.
Let's analyze the statements:
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 misleading. The investment increases by 2% each year, not 102%. A 102% increase would imply the amount would double and then some, which is not the case here.
3. **The initial deposit in the investment account was $1,550** - This is correct, as it matches the initial amount given in the function.
4. **The amount of money in the investment account decreases 2% each year** - This is incorrect. The factor \( 1.02 \) indicates growth, not a decrease. A decrease would be represented by a factor less than 1 (for example, \( 0.98 \)).
Therefore, the best interpretation is:
**The initial deposit in the investment account was $1,550.**
Let's analyze the statements:
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 misleading. The investment increases by 2% each year, not 102%. A 102% increase would imply the amount would double and then some, which is not the case here.
3. **The initial deposit in the investment account was $1,550** - This is correct, as it matches the initial amount given in the function.
4. **The amount of money in the investment account decreases 2% each year** - This is incorrect. The factor \( 1.02 \) indicates growth, not a decrease. A decrease would be represented by a factor less than 1 (for example, \( 0.98 \)).
Therefore, the best interpretation is:
**The initial deposit in the investment account was $1,550.**