Read the following personal letter. Answer each question. 7561 Knoxville Road Saddle River, New Jersey 07458 January 12, 1995 Dear Shannon, Thanks for your letter. Being president of the Computer Club takes a lot of time. If I had known you were going to move to Dallas and that I would have to replace you, I might never have let myself be elected vice president! Well, the big news is that I finally bought a CD-ROM drive for my computer. I hate to say it, but you were right. It’s fantastic! How did I ever live without one? I’ve already gotten a few games, and the graphics are unbelievable. Do you have any recommendations for multimedia encyclopedias? I want to get one. However, since they are expensive, I want to get advice from someone who knows something about them. Write back as soon as you can. Have you met any other computer nerds in Dallas? (Ha-ha, just kidding!) Your friend, Courtney Do you think Courtney and Shannon are good friends? Why?

Use the graphing package or your graphics calculator to graph and find the key features of the functions. Consider $f : x \mapsto 2 x+3$ or $y=2 x+3$ a. Graph the function. b. Find algebraically, the: i. x-axis intercept ii. y-axis intercept iii. slope. c. Use technology to check the axes intercepts found in b.

Set up the following equations for the computer:

Mathematical Equation:

a. A+B=5D

b. (X+Y)/4=Z

c. 5X-3Y=Z

Computer Equation:

a. D= A+B/5

b. (X+Y)/4

c. Z=5X - 3Y

Graphics are an effective way to communicate financial information. A stacked column chart is especially useful to present income statement data. The chart can show trends in sales, expenses, and net income for multiple fiscal years.

INSTRUCTIONS

5. What does the top of each column represent?

Use a calculator or computer to evaluate the integral.

$$\int_0^{10} 2^{-x} d x$$

Use the graphing package or your graphics calculator to graph and find the key features of the functions. Consider $f : x \mapsto 2^{x} .$ Graph the function and check these key features: a. as $x \rightarrow \infty, \quad 2^{x} \rightarrow \infty$ b. as $x \rightarrow-\infty, 2^{x} \rightarrow 0$ (from above) c. the y-intercept is 1 d. $2^{x}$ is > 0 for all x.

Given the fact that this patient works at a computer, what could be the cause of her pain?

Either click on the icon or use your graphics calculator (with the same scale on both axes) to plot $\left\{(x, y) : \quad x=\cos t, \quad y=\sin t, \quad 0^{\circ} \leqslant t \leqslant 360^{\circ}\right\}$ Your calculator will need to be set to degrees

Sketch the graph of each of the following exponential functions. Use a graphics calculator if available. Compare your graphs.

$$\text { i. } f(x)=2^x$$

$$\text { ii. } f(x)=5^x$$

$$\text { iii. } f(x)=\left(\frac{1}{2}\right)^x$$

$$\text { iv. } f(x)=\left(\frac{3}{4}\right)^x$$

Computer-Generated Images A computer-generated, square prism is made by constructing a square with vertices (0,0),(0,2),(2,2), and (2,0), and then translating it using $T:(x, y) \rightarrow(x+3, y+4)$, and connecting the vertices of the preimage to the corresponding vertices of the image. Find the volume of the prism.

Complete the depreciation schedule for computer software for Marker Graphics. The software cost $12,990, has an estimated life of 3 years, and has no salvage value.$

$$\scriptstyle\begin{array}{|c|c|c|c|c|c|c|} \hline&\text{End of} & \text{Original} & & \text{Annual} && \text{Accumulated} && \text{Book}\\ &\text{Year} & \text{Cost} & & \text{Depreciation} && \text{Depreciation} && \text{Value}\\ \hline15. &1 & \$12,990 & \text{a.} & & \text { b. }& &\text { c. } & \\ \hline 16. &2 & \$12,990&\text{a.} & &\text { b. }& & \text { c. } & \text {} \\ \hline 17. & 3 & \$12,990 &\text{a.}& &\text { b. } & &\text { c. } & \text {} \\ \hline \end{array}$$

$

(Turtle Graphics) The Logo language made the concept of turtle graphics famous. Imagine a mechanical turtle that walks around the room under the control of a C program. The turtle holds a pen in one of two positions, up or down. While the pen is down, the turtle traces out shapes as it moves; while the pen is up, the turtle moves about freely without writing anything. In this problem you’ll simulate the operation of the turtle and create a computerized sketchpad as well. Use a 50-by-50 array floor which is initialized to zeros. Read commands from an array that contains them. Keep track of the current turtle position at all times and whether the pen is currently up or down. Assume that the turtle always starts at position 0, 0 of the floor with its pen up. The set of turtle commands your program must process are shown in given figure. Suppose that the turtle is somewhere near the center of the floor. The following “program” would draw and print a

12-by-12 square:
2
5,12
3
5,12
3
5,12
3
5,12
1
6
9

As the turtle moves with the pen down, set the appropriate elements of array floor to 1s. When the 6 command (print) is given, wherever there’s a 1 in the array, display an asterisk, or some other character you choose. Wherever there’s a zero, display a blank. Write a program to implement the turtle graphics capabilities discussed here. Write several turtle graphics programs to draw interesting shapes. Add other commands to increase the power of your turtle graphics language.

$$\begin{array}{ll} \text { Command } & \text { Meaning } \\ 1 & \text { Pen up } \\ 2 & \text { Pen down } \\ 3 & \text { Turn right } \end{array}$$

$$\begin{array}{ll} \text { Command } & \text { Meaning } \\ 4 & \text { Turn left } \\ 5,10 & \text { Move forward } 10 \text { spaces (or a number other than } 10 \text { ) } \\ 6 & \text { Print the } 50 \text {-by- } 50 \text { array } \\ 9 & \text { End of data (sentinel) } \end{array}$$

For each of the following data sets, make sure the data is ordered and then find: (i) the median (ii) the upper and lower quartiles (iii) the range (iv) the interquartile range. 21.8, 22.4, 23.5, 23.5, 24.6, 24.9, 25, 25.3, 26.1, 26.4, 29.5. Check your answers using your graphics calculator.

Find the net price of the computer in the exercise discussed before.