Apps Allowing Exploration of The Exponential Function! Part 1.

Most of us are having to look at teaching via distance and most of us are not prepared for it.  I've spent my spring break exploring options for teaching classes this way but knowing my students, many of them won't worry about trying to keep up because they attend due to being under 16.  They see no reason for coming or doing the work.  So I've tried to find apps I can use to show these students that there are things they should know about including  I mentioned Creative Learning Exchange this past Friday but I want to spend more time on them because they have produced several  free apps which are well done and could easily be used in math classes.

 Retire Rich is an app that sets up a situation in which students are guided through the first two scenarios to determine which is better and in the process learn the program.

The story they provide is that Tara is thinking of putting away $1000 each year beginning at the age of 40 to 65.  She uses a fairly simple model and the app tells you the interest rate the account gets and it is basic.  When the program is run, she learns she won't get much more than $45,000 but if she does it from the age of 20 to 45, she'll end up with more than double what she would by waiting later.

After the second scenario, the student is encouraged to change the amount per year,  interest rate, or the ages of saving to see how these impact a person's final amount.

This means students can change variables to see how things change the overall picture.  How does interest rate change the final amount?  How does the amount saved change it?

What is even better is that students can double tap on each item for an explanation of part of it from interest to final amount.  The explanations include the basic mathematical information for each one.  In addition, there is a graph showing the growth of the retirement fund and a graph showing savings and interest.

This is a simplified model but it allows students to explore the concept of how to save the most amount within the shortest amount of time.  To make this more mathematically based, have students create a spread sheet with the same information to see if they agree with the figures produced by this app.  They can use the standard continuous interest or compound interest formulas to compare amounts.  This could  be turned into a project where students explore several scenarios and then create a prospectus for other students on planning for retirement.

The other app I want to look at today is Bacterial Sandwich.  This app looks at the growth of e coli in a sandwich.  The story is that someone packed a sandwich with 1500 bacteria in it at the beginning.  It looks at what happens to the bacterial when it is kept out in a room that is at 70 degrees.

Before having students run the actual model, the app goes through each factor in it and explains it clearly.

Then the app suggests the temperature be dropped to 68 degrees to see what the difference in growth is.  The student discovers the growth is significantly less under the second circumstance.

At the end, the student is again encouraged to  play with the different factors to see how it changes the final growth rate at the end.



This app even mentions that bacterial growth is exponential in nature.  So students are introduced to it in a safe way rather than being dropped into a problem in the chapter.

Instead of using a general problem giving the information, the problem appears in context with a real world situation.  In addition, students can play with this before they run the same numbers using the regular mathematical equations.

Once students are given the equation for bacterial growth, they can change the factors to see how these calculations match the answers from the app.

Both apps have a story setting up the context of situation and an explanation of the variables involved with the equations.  These are well done and easily understood by high school students of every level.

The nice thing about both of these apps is that they are both free and made to be used by both apple and android devices.  Wednesday, I'll review their two population apps to give you an idea of how they word.  Let me know what you think, I'd love to hear.