Question

The amount of money in a savings account is modeled by , where x represents the number of years. Predict the account balance after 0, 1, and 2 years. Round your answers to the nearest dollar.

Answer 1

To predict the account balance after 0, 1, and 2 years, we can use the compound interest formula. If the principal amount is $100 and the annual interest rate is 2%, the account balance after 0 years is $100, after 1 year is $102, and after 2 years is $104.04.

Step-by-step explanation:

To predict the account balance after 0, 1, and 2 years, we can use the compound interest formula. Let's consider an example where the amount of money in a savings account is modeled by the function A(x) = P(1+r)^x, where P is the principal amount, r is the annual interest rate, and x is the number of years.

For example, if the principal amount is $100, and the annual interest rate is 2%, the function becomes A(x) = 100(1+0.02)^x.

To predict the account balance after 0 years, we substitute x = 0 into the function: A(0) = 100(1+0.02)^0 = $100.

For 1 year, substituting x = 1 into the function gives: A(1) = 100(1+0.02)^1 = $102.

Similarly, for 2 years, substituting x = 2 into the function gives: A(2) = 100(1+0.02)^2 = $104.04.