MAT276 Modern Differential Equations Modeling Scenario 1 Consider a regular size bag of M&M candies (not...

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MAT276 Modern Differential Equations Modeling Scenario 1 Consider a regular size bag of M&M candies (not peanut, just regular). Usually there are about 55 pieces in each bag. They are of different colors, but each piece almost always has an "m" pressed on one side and not the other. Hence, there are distinctions between the sides. Let us conduct a couple of experiments (life and death experiments!) on the M&Ms. 1 Model 1: Death Model (sounds ominous, right?) Put 50 M&M's into a small container like a paper cup. First just read the description of the experiment. Before actually doing anything, describe what you think will happen and offer up some assumptions in support of your description, some which might not have that much to do with what you expect to happen. Description of the Experiment: (don't do it yet!) Gently shake the M&Ms out onto a flat surface like a desk (or you might want to use a paper plate to catch the M&Ms and keep them clean as well). We determine for each M&M if it lives or dies. If the m shows on top this M&M dies, otherwise there is life for this M&M. Upon death you should remove the M&M from the population (set these aside as we will need them for another experiment), count and note down the number of M&Ms who survive in Table 1, and thus put fewer M&Ms back into your container for the next iteration. Do this over and over and record your results. Questions: 1. State your assumptions about the physical activity. Many times assumptions run into each other, so break the assumptions down to their simplest form (i.e., do not use words like "and"). 2. Offer up a description (in words) of what should happen. Care to make a prediction about what happens in the long run? Adapted from 1-1-M&M-DeathImmigrationParameter Estimation, SIMIODE modeling scenario by Dr. Brian Winkel, Professor Emeritus, USMA, Director SIMIODE. 1 MAT276 Modern Differential Equations Modeling Scenario 1 Consider a regular size bag of M&M candies (not peanut, just regular). Usually there are about 55 pieces in each bag. They are of different colors, but each piece almost always has an "m" pressed on one side and not the other. Hence, there are distinctions between the sides. Let us conduct a couple of experiments (life and death experiments!) on the M&Ms. 1 Model 1: Death Model (sounds ominous, right?) Put 50 M&M's into a small container like a paper cup. First just read the description of the experiment. Before actually doing anything, describe what you think will happen and offer up some assumptions in support of your description, some which might not have that much to do with what you expect to happen. Description of the Experiment: (don't do it yet!) Gently shake the M&Ms out onto a flat surface like a desk (or you might want to use a paper plate to catch the M&Ms and keep them clean as well). We determine for each M&M if it lives or dies. If the m shows on top this M&M dies, otherwise there is life for this M&M. Upon death you should remove the M&M from the population (set these aside as we will need them for another experiment), count and note down the number of M&Ms who survive in Table 1, and thus put fewer M&Ms back into your container for the next iteration. Do this over and over and record your results. Questions: 1. State your assumptions about the physical activity. Many times assumptions run into each other, so break the assumptions down to their simplest form (i.e., do not use words like "and"). 2. Offer up a description (in words) of what should happen. Care to make a prediction about what happens in the long run? Adapted from 1-1-M&M-DeathImmigrationParameter Estimation, SIMIODE modeling scenario by Dr. Brian Winkel, Professor Emeritus, USMA, Director SIMIODE. 1