Question

Let y(t) represent your bank account balance in dollars after t years, starting with $20,000 and earning 6% interest annually. Express y(t) as a function of t.

Answer 1

y(t) represents the bank account balance after t years with a starting balance of $20,000 and 6% annual interest. The formula used to express y(t) is y(t) = $20,000(1.06)^t, which results from the compound interest formula.

Step-by-step explanation:

To express y(t), your bank account balance after t years, as a function of t, given an initial balance of $20,000 and an annual interest rate of 6%, you use the compound interest formula:

y(t) = P(1 + r/n)nt

Where P is the principal amount ($20,000), r is the annual interest rate (0.06), n is the number of times interest is compounded per year (annually, so n = 1), and t is the number of years.

Substituting the values, we get:

y(t) = $20,000(1 + 0.06/1)1*t

y(t) = $20,000(1.06)t

This function y(t) tells us the balance of the account after t years, with interest compounded annually.