Here's what the original page (where the Figure 2 graph came from) said: It actually represents the Michaelis-Menten equation, which arises in the study of enzymes. The curve given in Figure 2 is not about behavioral economics at all (nor is it about physics, as I suspected). Was Figure 2 hyperbolic or not? Enzyme Studies I didn't accept that Figure 2 was a hyperbolic curve at first because such curves usually have 2 arms, something like this: The hyperbolic curve appears to have infinite slope at S = 0, whereas the exponential ones do not.

You can see the hyperbolic curve is similar to our 'flipped' exponential decay ones, but not identical. The V max term in the hyperbolic curve above (Figure 2) was what made me think of these exponential curves. We've just flipped the exponential growth curve (that is, reflected it in a horizontal axis) from its usual shape (steeply descending at first, then levelling off). It's called an exponential 'decay' curve because the power of e is negative. The curve rises fairly quickly then flattens out to some limiting value (which in this case is 2 coulombs). Here's the graph of the charge from that example, given by q = 2(1 − e −10 t). A skydiver's velocity starts at zero, builds rapidly to around half of their final velocity, and as air resistance builds up, the velocity more gradually builds to some terminal value (usually around 200 km/h.)Īnother case is the charge in a circuit containing a capacitor (see Example 1 on that page). An example of such a curve arises in terminal velocity problems. It is the mirror image of an exponentially decaying quantity. An exponential decay (increasing form) curve describes situations where a quantity grows quickly at first, then levels out to some limiting value. Exponential decay (increasing form) graphsĪt first glance, this graph looked like an exponential decay (increasing form) to me. I began to suspect the author didn't really know what was going on in this topic (or certainly didn't understand the example graph). The subject matter of the graph suggested a physics application, rather than some behavioural finance model. That's when it started to get interesting for me. Then he immediately states the following, suggesting some relationship between the exponential curve above, and hyperbolic curves. The author correctly identifies an exponential curve and uses the following graph as an example (without saying what its relevance is, or indicating what the axes represent): Leaving the marketing behind for now, let's look at the mathematics used in the article. It's what marketers use all the time to encourage you to buy now. Most people would choose to claim a reward right now, rather than a larger reward some time in the future. In plain English, that's all hyperbolic discounting really means. Most people choose the immediate reward, because waiting for a month for a bit more doesn't seem to make sense. Question: If I offered you $100 today, or $105 in one month from now, which would you choose?

Well, I don't know that it's 'despicable' jargon (this is the kind of statement that discourages people from being comfortable with mathematics), and it worried me that a mathematical term was being maligned, so I read on. Since the phrase hyperbolic discounting is despicable jargon, let me explain it in terms that even I can understand.

The article is a case of someone using a mathematical term but not being quite sure what it means. I'd never heard of hyperbolic discounting and it looked mathematically interesting, so I followed the link. Thanks to dynamicsolo & RGV for helping me with this problem, I really appreciate your insights.I came across this article recently: Six Advantages of Hyperbolic Discounting…And What The Heck Is It Anyway? Does anyone have some advice for dealing with this form? This does no longer follow the form of the gamma function. The key difference being the term inside the exponential function. (a, b, c, d & g are real number constants) Here here a, b and c are constant and x>0.

I want to compute the integral of an empirical relation with respect to x, which I will refer to as y. If anyone could please assist in helping me with this problem my appreciation would approach infinity :) This function consists of many terms, but specifically, there is a term containing double exponential functions which is giving me some trouble. Hi, this is not really a homework problem, but something that came up during my research, upon trying to integrate some empirical function.

Exponential mathematica