Homework 1

Due: October 15, 2025
Points: 100

In the given examples, what you type is in redand the program prints what is in black. Your program output should look exactly like the output in the examples, except that what you type won’t be in red, and the results may differ in the last few digits.

1. (20 points) Currently, the U.S. tax code imposes a graduated income tax with deductions and credits. Occasionally, someone will propose a “flat tax,” which charges a fixed percent of income and has no deductions or credits. The figure most often quoted is 17%. Please write a program that asks the user to enter an income as an integer (no commas or periods!) and prints the amount of tax that would be paid on that income. Reject any negative incomes or input that is not a number.

   To turn in: Please turn in the program in the file flattax.py.

   Examples:

   
   What is the income? 124598
   The tax on income of 124598 is 21181.66
   

   
   What is the income? -250
   This doesn’t work for negative incomes like -250
   

   
   What is the income?  124,598
   Error – invalid input entered; put in an integer
   

   
   What is the income? 698321
   The tax on income of 698321 is 118714.57
   

2. (20 points) Now look at the current US tax scheme, which is a progressive tax. It works as follows:
   • If the income is less than or equal to $11,925, the tax is 10% of the income.
   • If the income is less than or equal to $48,475, the tax is 12% of the amount above 11,925 plus the tax that would be paid on the rest.
   • If the income is less than or equal to $103,350, the tax is 22% of the amount above $48,475 plus the tax that would be paid on the rest.
   • If the income is less than or equal to $197,300, the tax is 24% of the amount above $103,350 plus the tax that would be paid on the rest.
   • If the income is less than or equal to $250,525, the tax is 32% of the amount above $197,300 plus the tax that would be paid on the rest.
   • If the income is less than or equal to $626,350, the tax is 35% of the amount above $250,525 plus the tax that would be paid on the rest.
   • If the income is greater than $626,350, the tax is 37% of the amount above $626,350 plus the tax that would be paid on the rest.

   Reject any negative incomes or input that is not a number.

   To turn in: Please turn in the program in the file progtax.py.

   Examples:

   
   What is the income? 124598
   The tax on income of 124598 is 34846.020000000004
   

   
   What is the income? -250
   This doesn’t work for negative incomes like -250
   

   
   What is the income?  124,598
   Error – invalid input entered; put in an integer
   

   
   What is the income? 698321
   The tax on income of 698321 is 224227.52000000002
   

3. (20 points) Write a program to calculate the volume V of a test tube given its radius r and height h using this formula: V = π r² h

   Prompt the user for the radius and height, one per line. Both must be real numbers; they need not be integers.

   To turn in: Please turn in the program in the file testtube.py.

   Examples:

   
   Radius of base of cone: 1
   Height of cone: 5
   The volume of a cone with radius 1.0 and height 5.0 is 15.707963267948966
   

   
   Radius of base of cone: 2.3
   Height of cone: 3.4
   The volume of a cone with radius 2.3 and height 3.4 is 18.834895155822
   

   
   Radius of base of cone:  1/5
   Error – radius must be a real number
   

   
   Radius of base of cone:  1
   Height of cone:  3*4
   Error – height must be a real number
   

4. (40 points) In the SI model of disease spread, i(t)> is the proportion of the population that is infected at time t and β is the average number of people each infected person spreads the disease to each day. The equation modeling the spread is: i(t) =
   i(0)e^βt / 1 - i(0) + i(0)e^βt
   where i(0) is the proportion of the population initially infected. Assume each infected person spreads the disease to 1 uninfected person every 5 days, and initially 0.1% of the population is infected. The population is constant. Write a program that takes an integer as input, and computes the proportion of the population that is infected after that many days.

   To turn in: Please turn in the program in the file si.py.

   Examples:

   
   Number of days:  30
   After 30 days, the proportion of the population infected is 0.287664368675717
   

   
   Number of days: 40
   After 40 days, the proportion of the population infected is 0.7489923252324207
   

   
   Number of days: 10.3
   You must enter an integer number of days
   

Matt Bishop Office: 2209 Watershed Sciences Phone: +1 (530) 752-8060 Email: mabishop@ucdavis.edu

MHI 289I, Programming in Health Informatics Version of October 1, 2025 at 2:22PM

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