Demetrios opens an account with an initial investment of $2000. The annual interest rate is 5%. (a) If the interest is compounded continuously and Demetrios makes an additional$1000 deposit every year, what will be the balance at the end of 10 years? (b) If the interest is compounded quarterly (four times per year) and $250 is deposited at the end of each compounding period, what will be the balance after 10 years? (c) What happens if the interest is compounded daily?

Find all values of a such that det(A) = 0.

$$A=\left[\begin{array}{ll} -5 & 2 \\ 2 a & a \end{array}\right]$$

Use the simplex method to find the optimum strategy for players A and B and the value of the game for each payoff matrix.

$$\left[\begin{array}{rr} 1 & 0 \\ -2 & 4 \\ -1 & -1 \end{array}\right]$$

Powers of a square matrix can be found with matrix multiplication. The matrix $A^{2}=A A,$ that is, $A^{2}$ is the product of matrix A with itself. Find $A^{2}$ for each of the following matrices.

$$A=\left[\begin{array}{rrr} 1 & 0 & -3 \\ -1 & 2 & 0 \\ 3 & -1 & 2 \end{array}\right]$$

Convert A to echelon form, then find det(A) by tracking the row operations and computing the determinant of the echelon form.

$$A=\left[\begin{array}{rr} 3 & -2 \\ -1 & 2 \end{array}\right]$$

What is a semiconductor? How does it compare with a conductor and an insulator?

Find the radius of convergence of each of the series. $\sum_{n=0}^{\infty} \frac{x^{n+1}}{n !}$

In the following Problem, apply the successive approximation formula to compute $\operatorname{yn}(x)$ for $n \leqq 4$. Then write the exponential series for which these approximations are partial sums (perhaps with the first term or two missing; for example, $\left.e^{x}-1=x+\frac{1}{2} x^{2}+\frac{1}{6} x^{3}+\frac{1}{24} x^{4}+\cdots\right)$. $\frac{d y}{d x}=2 y+2, y(0)=0$

The height h (in feet) of a falling object at any time t (in seconds) is modeled by $h=-16 t^{2}+s_{0},$ where $s_{0}$ is the initial height (in feet). Use the model to find the time it takes for an object to fall to the ground given $s_{0}$. $s_{0}=48$

Find a particular solution to the given second-order differential equation. $x^{\prime \prime}-2 x^{\prime}-3 x=4 e^{3 t}$

Determine whether each of the following statements is true or false, and explain why. The sample mean $\bar{x}$ is not the same as the population mean $\mu.$

Electrons and positrons collide from opposite directions head-on with equal energies in a storage ring to produce protons by the reaction $e^{-}+e^{+} \rightarrow p+\bar{p}$ The rest energy of a proton and antiproton is 938 MeV. What is the minimum kinetic energy for each particle to produce this reaction?

Sketch the graph of the function with the given rule. Find the domain and rang of the function.

$$f(x)=\left\{\begin{array}{ll} -x+1 & \text { if } x \leq 1 \\ x^{2}-1 & \text { if } x>1 \end{array}\right.$$

Evaluate the radical expression. If not possible, state the reason. $\sqrt[3]{-125}$