f : R → R , x ↦ a b x for the case a&gt;0 and b&gt;1.I`m interested in other examples which are in some way fascinating or funny for this case.I don't want any discrete examples or such involving the Euler number e. Any suggestions for that?

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f  :      R    →      R    ,    x  ↦  a      b    x  for the case a&amp;gt;0 and b&amp;gt;1.I`m interested in other examples which are in some way fascinating or funny for this case.I don&#039;t want any discrete examples or such involving the Euler number e. Any suggestions for that?

h2a2l1i2morz · Accepted Answer

a&amp;gt;0  and b&amp;gt;1 correspond to exponential growths. Thius kind of formula is used in studies about population, virus, bacteria, ...But you have one case which is very common : make a deposit of a dollars on your bank account and let us suppose that the bank gives you an interest of r% per year. After n years, your initial a dollars will become   a            (      1      +              r        100            )        n   dollars.Now, if your bank is generous and if you are patient, you will be rich. Suppose that you invest today 100 dollars, that your generous bank gives you a 5 % interest (give me its name) and that you are ready to wait for 20 years, then, in year 2034, you will be able to cash 265 dollars.Unfortunately, with bacteria and virus, this goes much faster. For example if we start with only one bacteria which can double every hour, by the end of one day we will have almost 17 million bacteria.

f:R->R,x->ab^x for the case a>0 and b>1. I`m interested in other examples which are in some way fascinating or funny for this case. I don't want any discrete examples or such involving the Euler number e. Any suggestions for that?

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