EXERCISES:
problem 1: Make a program that will graph the following parabolas where x ranges from -10 to 10 in increments of 0.1. Make each parabola a different color and put all the parabolas in the same figure or graph. You can do this by using the “hold” function (Use the “help” to learn how to do this). Use the “help plot” to find the code for the different colors and the “help legend” to show how to put the legend in the figure plot. The colors for each line are given below.
a) x^{2} – 6x + 5 black
b) -x^{2} – 4x – 3 blue
c) x^{2} + 6x + 8 red
d) 0.5x^{2} – 2x + 4 green
Do not forget to put a pause after this.
problem 2: The decay equation for a radioactive isotope is given by Q(t) = Q(0)e^{-λt}, where Q(0) is the initial quantity (at t = 0), λ is the radioactive decay constant and t is the time. Carbon 14 has a decay constant λ = 0.00012097/year. Create a program that, if you had 15 gms of Carbon 14 at time 0, plotsthe following two figures side-by-side in one figure window (using the “Subplot” function):
• The decay curve for time t = 0 to 1,000,000 years in steps of 1 year. Do not forget to label the axes with units (x-axis = years; y-axis = gms) and create a title called “Decay Curve As A Function Of Time” for the plot.
• The curvewith the x-axis in logarithmic scale (HINT: Look into the function “semilogx” for the graphing).
Do not forget to put a pause after this.
problem 3: In 2007 individuals in the United States of America paid the following income taxes. prepare a program to find out how much income tax a person will owe based on this information in the table below. The program should accept a total income figure from the user and find out the income tax.
In this program, the program will ask “What is your income?”. After you input the income, the program output is going to say “Your tax for this income is $????.??”
(????.?? is whatever output the program computes based on the income input into the program and the table above).