Technically, an exponent is a number that tells you how many times another number, called the ‘base’, is multiplied by itself. For example, 2 exp 4 tells us to multiply 2 (the base) by itself 4 times, yielding the number 16. The exponent is sometimes referred to as ‘the power’. We might say, ‘2 to the power of 4’.

Fair enough.

Functionally, it’s the *multiplying-by-itself *thing that bends the curve and creates acceleration in values. In linear arithmetic, the first four products are 2, 4, 6, 8. But in exponentials, the first four products are 2, 4, 8, 16; clearly the exponential expression is not linear.

What that means is that* As you move away from the present point, things accelerate quickly**‘*.

**Consider project communications**:

The number of ways that N people (or systems or interfaces) can communicate is N*(N – 1), which for large N is approximately N x N, or N-squared (an exponential, N with an exponent of 2).

**Consider project finance:**

The present value of future business benefits of a project are discounted, exponentially, by the expected risk.

Financiers think of risk in terms of the ‘rate of return’ they demand in order to agree to commit capital to a risky project.

And, this rate of return, “r”, is compounded over time. Compounding means that [1 + r] exponentially decreases with the number of compounding periods. The future value is “discounted” to a present value by that decreasing factor.

**Consider risk management:**

The idea that risk inversely compounds exponentially with time, and thereby discounts the value of future decisions and outcomes is a commonly held concept in risk management.

Other types of risk are subject to exponential effects. For example, the density of probable failures in the future is inversely and exponentially related to a present value of the failure rate.

**Consider the so-called “bell curve”**

The ‘bell curve’ shows us the effects of natural clustering of random outcomes or observations around the mean value.

The actual formula for the curve is non-linear to be sure, and usually we just look up values we are interested in, which for the most part delineate confidence intervals.

**Consider schedules at the milestone**

**Consider the random arrival rate **of independent actors (events)

Again, the probability distribution of random arrivals is an exponential, and an important concept in certain elements of risk management (Earthquake prediction, to name one, but other types of failures as well).

**Consider ‘utility’**

—————–

If you look up Bartlett’s book, you’ll find most of the chapters are available free in pdf format

Shout-out to herdingcats for the quotation

Footnote for the math inclined or curious:

*It’s common to think of the number ‘2’ as 2 with an exponent of 1 (any number with an exponent of 1 is equal to itself); and the number ‘1’ is 2 with an exponent of 0 (any number with an exponent of 0 is equal to 1). Other examples: The number ‘4’ is 2 with an exponent of 2; the number ‘5’ is 2 with an exponent of about 2.35, but also 5 is the number 10 with an exponent of about 0.7.*

*And, a negative exponent is mathematically equivalent to division: 1 divided by the exponential. For example, 0.5 is just 2 with -1 as the exponent, usually written as 1/2.*

*But here’s a limitation of exponent math: there is no exponent that will give us exactly the number ‘0’, although we can get pretty close with an arbitrarily large negative exponent. *

*Now the “base” doesn’t always have to be ‘2’. If we change the base to 10, the number 2 is now 10 with an exponent of approximately 0.3. (somewhat like there is no exponent that gives us exactly the number 0, there is no exponent of 10 that gives us exactly the number 2. This is the reason that financial reports and other resource reports are not computed with exponential math. Such reports require exact numbers, not approximations)*

*You may have heard the expression that “things are logarithmic”. That’s another way of expressing the idea of an exponential. The ‘logarithm of 2 (in base 10) is equal to 0.3′. That statement is equivalent to saying ’10 with an exponent of 0.3 is equal to 2’.*

Like this blog? You’ll like my books too! Buy them at any online book retailer!