In 2000, 100 is invested in a savings account, where it grows by accruing interest that is compounded annually (once a year) at an interest rate of 5.5$\%$. Assuming no additional funds are deposited to the account and no money is withdrawn, give a formula for a function describing the amount $A$ in the account after $x$ years have elapsed. Define when the function $f(x)$ is odd and even. Also, define when a function $f(x)$ is increasing and decreasing? If $y = x^2$ is a given function then determine the interval in which the function is increasing and decreasing and draw the graph of the given function. [5+5]

A rock breaks loose from the top of a tall cliff. Find average speed during the first 2 sec of fall. What is its average speed during the 1sec interval between second 1 and second 2? Find the speed of the falling rock at $t = 1$ and $t = 2$. [3+3+4]

Find the positive root of the equation $f(x) = x^2 - 2 = 0$. Find the Taylor series and the Taylor polynomials generated by $f(x) = e^x$ at $x = 0$. Use the Trapezoidal Rule with $n = 4$ to estimate $\int_{1}^{2} x^2 dx$. Compare the estimate with the exact value. [3+3+4]