Thursday, October 30, 2008

Strategies for solving Small World Unit Problem

Yesterday we said the general form for exponential functions is:

Today in class we discussed several strategies to help us solve our Unit Problem for Small World.

Recall that we need to find out when the population will reach the point that we are all "squashed up". Earlier we said that this will happen when our population reaches 1.6x10^15 people. We decided that population growth was best modeled by an exponential function.

What strategies did we discuss?

  1. One was to input our data from the tables into the calculator. Here is a sheet of instructions to enter data into the calculator. Then we could guess equations that fit our data the best -- like "Tweaking this Function".

  2. Another way was to do something similar to HW25 and HW29. Use two of the data points and solve for the variables k and c. Some people said that in order for this strategy to work, we would have to set one of our years to 0, just like HW25 and HW29.

  3. An even different approach is to use the calculator's regression feature. I am not advocating this approach, but it is a valid approach. However, you may need to do some calculations to convert the equation into the form we want the final answer to be in.

Ok.Ok.Ok. Say we use one of those strategies. And say we get an exponential equation that models our data really well. Then what? Are we done? Have we solved the unit problem?

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