Question

In the exponential equation f(0) = 300 * 1.03, what does the value 1.03 represent?

A. the initial amount of money deposited in the account
B. the dollar amount that will be added to the account each year
C. the factor by which the amount of money in the account is multiplied each year
D. the exponent to which the amount of money in the account is raised each year

Answer 1

In the equation f(0) = 300 × 1.03, the value 1.03 represents the factor by which the account balance is multiplied each year due to compound interest, reflecting a 3% annual interest rate.

Step-by-step explanation:

In the exponential equation f(0) = 300 × 1.03, the value 1.03 represents the factor by which the amount of money in the account is multiplied each year. This factor includes the original amount plus an additional 3% which is the interest added to the account after one year.

The process described here is very similar to the concept of compound interest, where the initial deposit grows over time by being multiplied by a certain factor representing the annual interest rate.

For instance, if you start with $300 and the account has a 3% annual interest rate, after one year you would have the initial amount times 1.03, which becomes $300 × 1.03 = $309. In the subsequent year, this amount would again be multiplied by 1.03, demonstrating the principle of compound interest as the interest is calculated on the new total, not just the initial deposit.