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# Exponential decay of gas prices: A logarithm and inverse case study

Author: Christopher Danielson
##### Description:

To support students working on an assignment dealing with exponential decay in a College Algebra class.

An exponential equation is solved by use of logarithms, and students are encouraged to consider the meanings of these equations and their solutions.

(more)

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Tutorial

## Introduction (c)    Based on the news report that \$3.60 represents a 10% drop from the previous week, what was the price of gas one week before this report?
(d)    Part a asks you to assume that the relationship between time and the price of gas during this time period is exponential. In an exponential model, the decay factor (i.e. first ratio) will be constant over time. Assume instead that it the drop in price is linear. That is, assume that instead of a constant decay factor, we have a constant first difference. Create a linear model for this relationship.
(e)    Graph your linear and your exponential models on the same set of axes.

Source: Stewart, Redlin, Watson and Panman. (2011). College algebra: Concepts and contexts. Belmont, CA: Brooks/Cole.

## A student's question

After class today, a student asked me about solving the following equation: The following video demonstrates the solution method.

## Solving the equation

This video shows the symbolic solution to the equation.

## Now let's step back for a moment

So now we have a solution. What we need to do is interpret the solution. Important questions to consider include these: