The exponential function with base e is called the natural exponential function. This base is used in economic analysis and problems involving natural growth and decay.

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.

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.

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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 ourWorksheet: Logarithmic Function 1.

Find the value of y. (1) log 5 25 = y (2) log 3 1 = y (3) log 16 4 = y Write the following equalities in exponential form.

(1) log 3 81 = 4 (2) log 7 7 = 1 (3) log 1 2 1 8 = 3 (4) log 3 1 = 0 (5) log 4 1 64 Draw the graph of each of the following logarithmic functions, and analyze each of them.

§ Algebra I, Adopted (One Credit). (a) General requirements. Students shall be awarded one credit for successful completion of this course. The exponential form Introduction In addition to the cartesian and polar forms of a complex number there is a third form in which a complex number may be written - the exponential form.

Mar 27, · We'll again touch on systems of equations, inequalities, and functions but we'll also address exponential and logarithmic functions, logarithms, imaginary and . Improve your math knowledge with free questions in "Convert between exponential and logarithmic form" and thousands of other math skills.

Write Exponential Functions. Showing top 8 worksheets in the category - Write Exponential Functions. Some of the worksheets displayed are Exponential functions date period, Concept 17 write exponential equations, 11 exponential and logarithmic functions work, Work logarithmic function, Graphing exponential, Work on solving problems on exponential functions, Work exponentials and .

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Relationship between exponentials & logarithms (video) | Khan Academy