The Biology and Math Interface Group Presents…

Our Teachable Tidbit Topic: Exponential growth and decay with applications to biology Learning Outcomes From Tidbit: The student should be able to: Fit an exponential model to data Make predictions using an exponential model Interpret components of a exponential model Do sensitivity analysis Read, understand, and know how to graph an exponential function

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 What the instructors and students need to know

Content Presented Prior to Tidbit

Video tml#/home

Activity Introduction... 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.

In the year 1995 the population equals 75 if the growth rate is 0.65, calculate the population in the year 2011.

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

Find the equation for the exponential population curve above.

Homework and Extension Ideas Example of an isomorphic homework assignment Extension ideas?????