Question

A high-interest banking account pays 6% interest per year. Jack deposits $250 into the account at the beginning of the year. He wants to create an equation that would calculate how much money is in the account after a certain number of years.

What is the base of the exponential equation Jack would use in this situation

Group of answer choices

0.06

1.06

250

6

Answer 1

In this situation, the amount of money in the account grows due to the interest rate over time. The formula for compound interest can generally be expressed as:

\[ A = P(1 + r)^t \]

where:
- \( A \) is the amount of money accumulated after \( t \) years, including interest.
- \( P \) is the principal amount (the initial deposit).
- \( r \) is the interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.

For Jack's account:
- The principal \( P = 250 \) (the initial deposit).
- The interest rate \( r = 0.06 \) (6% as a decimal).

So, the equation becomes:

\[ A = 250(1 + 0.06)^t \]

This simplifies to:

\[ A = 250(1.06)^t \]

In this equation, the base of the exponential component is \( 1.06 \), which accounts for the initial amount growing at the annual interest rate.

Therefore, the correct choice for the base of the exponential equation is:

**1.06**