Banking Tomasita deposited $1000 in an account at the beginning of 2001. The account had a 3% interest rate, compounded quarterly. The table below shows her balance after each quarter of the year.
a. In an account where the interest is only compounded once per year, the balance after x years is given by P(1 + r)x, where P is the amount invested and r is the interest rate as a decimal. Find the interest rate with an annual compounding that would result in the balance that Tomasita had at the end of one year. This interest rate is called the effective rate.
b. Find a function that models the amount in Tomasita's account. Let x be the number of years since the beginning of 2001.
c. Write the equation from part b in terms of base e.
d. What interest rate with continuous compounding would result in the balances shown for Tomasita's account?