Write an exponential function in logarithmic form and exponential form

However, if we put a logarithm there we also must put a logarithm in front of the right side. This is commonly referred to as taking the logarithm of both sides.

In this article we will show that progressive estimation scale, like Fibonacci sequence often used by agile teams, is more efficient than linear scale and provides the team with more information about the size of backlog items.

Intro to Logarithms (article) | Khan Academy

We will use pretty basic principles of Information Theory to arrive at our results. Also we will formulate a hypothesis about normalization of the estimation base.

Most often it would be Modified Fibonacci Sequence: Less common is the scale used by XP proponents: We call them progressive to reflect the fact that the values grow much faster than linearly.

Modified Fibonacci sequence approximated by exponential function for its range of values.

As we well know, thousands of agile teams are applying these estimation scales very successfully. What makes exponential scale so useful? We used to answer this question by referring to the fact that the bigger the size of a backlog item say, N story points the harder it is to say the difference between N and N — 1.

However the statement itself is not a fundamental axiom but is just a corollary of more generic principles, which we are going to consider. U is an arbitrary backlog item; L — maximum possible size of any backlog item from the backlog; P — absolute precision of estimation; the point on the horizontal axis linked to item U shows its size.

As we well know from the basics of Information Theory, information also called mutual information of two experiments, see http: So now it is easy to interpret the amount of information enclosed in experiment A as the amount of uncertainty it reduces about experiment B.

The other one A consists in applying our estimation technique and thus reducing the uncertainty to certain extent i. This latter equation gives us very interesting result: More specifically, it grows as quickly as logarithm function.

Logarithmic behavior of information about the size of an item as a result of estimation process. And finally using exponential or close to exponential estimation scale becomes totally logical — it adds valuable information faster. We can hope though that teams are able to empirically find the right usage of the Fibonacci scale to be able to obtain information efficiently.

For further simplicity and as we shown before we can use certain exponential function instead of Fibonacci sequence. Blue graph stands for old scale of estimation and red one stands for the new one.

This by the way means that: Changing the estimation basis in Fibonacci sequence is quite a responsible thing, often underestimated.

It may get the team closer or further from efficient estimation. But now we can consider an interesting fact that many agile teams could confirm: This of course depends on the team size and would be smaller for the smaller teams and bigger for larger teams.

But maybe this is just the way teams optimize their estimation basis over time to efficiently manage the potentially available information. Based on this we formulate our Agile teams that normalize their estimation base over time, likely arrive at their optimal estimation capability from the standpoint of information that they acquire about the backlog items they estimate.

Although it looks like a bit of a journey to get to a better estimation base, we know we have simple stupid but reliable method to get started.Writing Exponential and Logarithmic Equations from a Graph Writing Exponential Equations from Points and Graphs.

Exponential distribution - Wikipedia

You may be asked to write exponential equations, such as the following. Definition of Exponential Function The function f defined by. where b > 0, b 1, and the exponent x is any real number, is called an exponential function. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

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In this section we will introduce logarithm functions. We give the basic properties and graphs of logarithm functions. In addition, we discuss how to evaluate some basic logarithms including the use of the change of base formula.

We will also discuss the common logarithm, log(x), and the natural logarithm. If you want to solve a logarithm, you can rewrite it in exponential form and solve it that way! Follow along with this tutorial to practice solving a logarithm by first converting it to exponential form.