A Log’s Purpose
As we continue to think about modeling with mathematics, there are some situations where we do more than just model a set of data or a graph with a function. Sometimes we use an existing model in a context to create a different model that relates the variables in a different way. This gives us different things to solve for and a unique way to represent the situation with graphs.
The list gives some scenarios we can use exponential functions to model. Study each scenario and the function that models it, then answer the questions that follow:
I picked "The chess club started with a membership of only 4 students, but the membership grew at a rate of 2.56% each week. The number of students is modeled by f(x) = 4(1.0256)x."
Questions:
Part A
Choose one of the scenarios from the list, and create a question you could ask that could be answered only by graphing or using a logarithm.
Part B
Using logarithms to find the answer to the question in part A.
Part C
Let your dependent variable in the function be y. Write the function that models the independent variable in terms of y, using logarithms.
Part D
Plot the graph of the logarithmic function you wrote in part C.
Part E
We know that logarithmic functions are a bit more unusual than functions we’ve seen in the past, such as linear, exponential, quadratic, and even polynomial and radical functions. We rarely see them in examples, so what’s their real purpose as functions?
