The Biology and Math Interface Group Presents…. Our Teachable Tidbit Topic: Exponential growth and decay with applications to biology. Learning Outcomes F rom T idbit: The student should be able to: Fit an exponential model to data Make predictions using an exponential model
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Learning Outcomes From Tidbit:
The student should be able to:
Overall Goals for Unit: Students will appreciate the importance of mathematics in modeling biological processes
Skill Level of Students: This tidbit can be used in a college calculus course or an introductory biology class
What we assumed: Students have little to no prior experience with college level biology, but students have been exposed to logarithms and exponentials
If we let P define the number of people infected lets look at a way we can model the spread of infection starting with Gwyneth Paltrow…
Each group should have two cups, one with pennies and one without. We will be simulating a model of exponential growth, that is the spread of disease, by flipping the pennies and adding a penny for every head.*
Begin with one penny, the initial infected individual. Your group will need a scribe, someone to flip pennies, and someone to add pennies.
*Exponential decay can also be modeled using pennies just begin with all pennies instead of one and remove a penny for every heads or tails.
Suppose we have two diseases spreading through two different populations. Disease A’s propagation is identical to disease B, except disease B has a k value twice as big as disease A. How is the population of people affected by disease A compared to disease B?
A. Population of A is twice the population of B
B. Population of B is twice the population of A
C. Both populations are the same
D. Not enough information given to determine populations
E. None of the above
Example of an isomorphic homework assignment