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.

Question

`A\left(t\right)=1,550\left(1.02\right)^{t}`
Which statement best interprets one value of the function?
a. the initial deposit in the investment was $1,581.
b. the amount of money in the investment increases by 102% each year.
c. the initial deposit in the investment was $1,550.
d. the amount of money in the investment decreases by 2% each year.

Answer 1

To interpret the function \( A(t) = 1,550(1.02)^t \), let's look at each statement:

a. The initial deposit in the investment was $1,581. - This is incorrect because the initial deposit is represented by the coefficient in front of the parenthesis, which is $1,550.

b. The amount of money in the investment increases by 102% each year. - This is incorrect. The investment increases by 2% each year, not 102%.

c. The initial deposit in the investment was $1,550. - This is correct. At \( t = 0 \) (the start), the equation gives \( A(0) = 1,550(1.02)^0 = 1,550 \).

d. The amount of money in the investment decreases by 2% each year. - This is incorrect. The investment does not decrease; it increases by 2% each year.

Therefore, the statement that best interprets one value of the function is:

c. the initial deposit in the investment was $1,550.