Question
an investor deposited money into an investment account that earns interest comnpounded 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?
a the initial deposit in the investment account was $1,581
b the amount of money in the investment account increases 102% each year
c the initial deposit in the investment account was $1,550
d 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?
a the initial deposit in the investment account was $1,581
b the amount of money in the investment account increases 102% each year
c the initial deposit in the investment account was $1,550
d 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 investment account after \( t \) years.
Let's analyze the options:
a) **The initial deposit in the investment account was $1,581.**
- This is incorrect. The initial deposit is represented by the constant \( 1,550 \) in the function.
b) **The amount of money in the investment account increases 102% each year.**
- This is incorrect. The function shows that the amount increases by 2% each year, not 102%.
c) **The initial deposit in the investment account was $1,550.**
- This is correct. The value \( 1,550 \) is indeed the initial deposit when \( t = 0 \).
d) **The amount of money in the investment account decreases 2% each year.**
- This is incorrect. The account actually grows by 2% each year, not decreases.
Therefore, the best interpretation of one value of the function is:
**c) The initial deposit in the investment account was $1,550.**
Let's analyze the options:
a) **The initial deposit in the investment account was $1,581.**
- This is incorrect. The initial deposit is represented by the constant \( 1,550 \) in the function.
b) **The amount of money in the investment account increases 102% each year.**
- This is incorrect. The function shows that the amount increases by 2% each year, not 102%.
c) **The initial deposit in the investment account was $1,550.**
- This is correct. The value \( 1,550 \) is indeed the initial deposit when \( t = 0 \).
d) **The amount of money in the investment account decreases 2% each year.**
- This is incorrect. The account actually grows by 2% each year, not decreases.
Therefore, the best interpretation of one value of the function is:
**c) The initial deposit in the investment account was $1,550.**