Question

The amount of money, A, earned after being compounded monthly for t years with Eaton National Bank is represented by the function f(x)=4,000(1.0056)12t .Select the correct answers from the lists.(2 points)The initial amount of money invested is $. The function represents an exponential  model where the amount of money in the account increases by % each year.

Answer 1

To analyze the function \( f(t) = 4000(1.0056)^{12t} \):

1. **Initial Amount of Money Invested:** The initial amount of money invested is represented by the coefficient of the function. In this case, it is:
\[
\text{Initial amount} = 4000 \, \text{dollars}
\]

2. **Exponential Growth Rate:** The term \( (1.0056)^{12t} \) indicates compound interest. The base of this exponent, which is \( 1.0056 \), can be converted to a percentage increase per time period (in this case, per month).

To find the annual growth rate, we can calculate:
\[
(1.0056)^{12}
\]

To simplify, let's compute this:
\[
(1.0056)^{12} \approx 1.0673 \quad \text{(using a calculator)}
\]

The annual growth rate, as a percentage, is then:
\[
(1.0673 - 1) \times 100 \approx 6.73\%
\]

So, to summarize:

- The initial amount of money invested is **$4,000**.
- The function represents an exponential model where the amount of money in the account increases by approximately **6.73%** each year.