Agenda

1. See how functions can be used for scientific calculations.
2. Review for quiz on functions on Monday, April 27th.
3. Practice with scientific calculations.

The size of living cells is limited by the surface area to volume ratio. The following function calculates the ratio of a rectangular solid given its width, height, and length.

def surface_area_to_volume_ratio(width, height, length):
    surface_area = 2 * ((width * height) + (width * length) + (height * length))
    volume = width * height * length
    return surface_area / volume

There is a program called sa_explorer.py in the example program repository that you can run to see how different cell sizes affect the surface area to volume ratio.

If you start with one bacterium, how many do you have after a certain number of generations? If you assume that each bacterium divides every generation, and none of them die, this program will print out the generations.

num_generations = 100
num_bacteria = 1
for generation in range(1, num_generations + 1):
    print(f"Generation # {generation} population = {num_bacteria}")
    num_bacteria *= 2

It turns out that the number of bacteria after n generations is 2 ** n. Therefore, we can have a function to calculate the population quickly using this definition.

def population(generation):
    return 2 ** generation

We will have a quiz over functions on Monday, April 27th. It will be multiple choice with 30 questions and will count 15 points. Here are the things you need to study:

• PowerPoint of Functions lecture
• Functions Worksheet with Answers
• Lessons on Functions with Turtle Graphics: 4/9, 4/13, 4/16, and 4/20.