Exponentials

Homework 6
Below is a scatter plot with both a linear model and an exponential model for a data set for 6-sided dice (like we did in class). The data was created by rolling 6 sided dice, removing any dice that rolled a “1” and recording how many dice were remaining.

Does a linear trendline look unreasonable for this data? Why or why not?

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Does an exponential trendline seem unreasonable for this data? Why or why not?

Write down the linear model for this data and describe what each of the values in the model mean for this dice rolling context.

y = _____________________

Write down the exponential model for this data.

y = ________________________

Calculate the e^bvalue (round to 4 decimal places): e^b = __________
Using e^b= rrewrite this model in the form y = a*R^x

y = ______________________

Describe what each of the values (including the variables) in the y = a*R^x model mean for this dice rolling context.

Which value in the exponential model represents something similar to the y-intercept of a linear model? Explain how they are similar.

Which value in the exponential model represents something similar to the slope of a linear model? Explain how they are similar.

Suppose we start with 1,500 dice and as we roll them, we remove dice that are rolled a 1. Fill in the table below with the appropriate theoretical model for how many dice will be remaining after x rolls, depending on how many sides the dice have:
Dice Model in the form y = a*R^x
5-sided

13-sided

10-sided

Suppose we change the rule of decay and say that we will remove a dice if it is rolled the highest possible value. Explain why the models above also work for this situation.

What if we remove not only dice which roll a 1, but we also remove any dice which roll a 2. Fill in the table below with the appropriate theoretical model for how many dice will be remaining after x rolls.

Dice Model in the form y = a*R^x
5-sided

13-sided

10-sided

How did the models change and why?

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