This is worth 10 points. Please pay attention to the numbers and lettered sections of the problem set description because that is how it will be graded. Add any additional information that you like. I've designed this problem set to follow the lecture notes and to build from what I think is easiest to harder.

This is due at the beginning of class. Anything after that will be treated as late.

1. (2 points) Iterative model of "constant growth".

a. Create a graph of pigs vs. time by iteratively calculating the population. Use a 0.2 growth rate, starting with 100 pigs for ten time steps. Do this by hand or in Excel and graph it.

b. Create a graph that has this same growth rate as an exponential function (N = N0e^rt). Compare this to the previous graph. Why are they different?

 

2. (3 points) Michaelis-Menten sub-model:

a. Create an Excel chart of the growth rate vs. resource concentration given the following information: Vmax = 0.10, Km = 20. Write out the equation and calculate the growth rate for a range of resource concentrations.

b. In your own words, describe what Vmax and Km mean.

c.Use this equation to create a velocity vs. resource chart with resources from resources = 0 to 100.

 

3. (3 points) Use Excel to create an iterative model for resource depletion like we did in class. You will need a column to calculate the time, resources, resources_taken_up, and population. Start with 10 units of population and 90 units of new resources. Use the Michaelis-Menten model (as above) with Vmax per individual = .15 and the Km = 10. Please see the spreadsheet linked from lecture 3 to see an exmaple of how to put this together.

a. Provide the table that shows the calculations for the first 20 time steps

b. Make a correction to the time_step to keep the model from going to negative resources

c. Show the graph of resources and population against time.

 

4. (2 points) Make an Excel spreadsheet of the Logistic equation for similar values as in problem 3. Please refer to the example spreadsheet that is linked from the notes in Lecture3. Use:

max_growth_rate =0.15
initial_population=10
carrying_capacity=100

a. Show the calculation table and a graph of population vs. time

b. describe the differences between the "resource depletion" model (question 3) and the "logistic" model (question 4).