Examples of exponential growth

Examples of exponential growth
ตัวอย่างของการเติบโตแบบเอกซ์โปเนนเชียล
Biology. ชีววิทยา
Microorganisms in a culture dish will grow exponentially, at first, after the first microorganism appears (but then logistically until the available food is exhausted, when growth stops).
จุลินทรีย์ ในถ้วยเพาะเลี้ยงจะเติบโตแบบเอกซ์โปเนนเชียลอย่างสม่ำเสมอเว้นแต่เมื่อ ทรัพยากรและพื้นที่ไม่จำกัด
Many responses of living beings to stimuli, including human perception, are logarithmic responses, which are the inverse of exponential responses; the loudness and frequency of sound are perceived logarithmically, even with very faint stimulus, within the limits of perception. This is the reason that exponentially increasing the brightness of visual stimuli is perceived by humans as a smooth (linear) increase, rather than an exponential increase. This has survival value. Generally it is important for the organisms to respond to stimuli in a wide range of levels, from very low levels, to very high levels, while the accuracy of the estimation of differences at high levels of stimulus is much less important for survival.
การตอบสนองของสิ่งมีชีวิตต่อสิ่งเร้า รวมถึงการรับรู้ของร่างกาย ก็สามารถใช้สมการลอการิทึมคำนวณได้(อินเวิร์สของฟังก์ชันเอกซ์โปเนนเชียล) ความดังและความถี่ของคลื่นเสียงถูกรับรู้อย่างลอการิทึม ความสว่างของแหล่งแสงที่เติบโตอย่างเอกซ์โปเนนเชียลจึงปรากฏแก่สายตามนุษย์เหมือนเติบโตแบบเส้นตรง สิ่งมีชีวิตจึงสามารถรับรู้แสง สี เสียง ในปริมาณน้อยมาก
Computer technology เทคโนโลยีคอมพิวเตอร์
In computational complexity theory, computer algorithms of exponential complexity require an exponentially increasing amount of resources (e.g. time, computer memory) for only a constant increase in problem size. So for an algorithm of time complexity 2^x, if a problem of size x=10 requires 10 seconds to complete, then a problem of size x=11 will require 20 seconds, and x=12 will require 40 seconds. This kind of algorithm typically becomes unusable at very small problem sizes, often between 30 and 100 items (most computer algorithms need to be able to solve much larger problems, up to tens of thousands or even millions of items in reasonable times, something that would be physically impossible with an exponential algorithm). Also, the effects of Moore's Law do not help the situation much because doubling processor speed merely allows you to increase the problem size by one. E.g. if a slow processor can solve problems of size x in time t, then a processor twice as fast could only solve problems of size x+1 in the same time t. So exponentially complex algorithms are most often impractical, and the search for more efficient algorithms is one of the central goals of computer science.

Physics
Nuclear chain reaction (the concept behind nuclear weapons). Each uranium nucleus that undergoes fission produces multiple neutrons, each of which can be absorbed by adjacent uranium atoms, causing them to fission in turn. If the probability of neutron absorption exceeds the probability of neutron escape (a function of the shape and mass of the uranium), k > 0 and so the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction.