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Please accept my apology in advance as i am not very good in math. I am looking for equation for my simulation that gives the exponential behavior in the initial x-axis points and turned to linear behavior as we moved on. For example there is a graph of Range (0,0) to (10,10). Now i am looking for equation that gives me exponential increase behavior until the x value is 5 then turned it behavior to linear. waiting for your valuable suggestions. Thanks

Hans Lundmark
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user2293224
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  • You mean something like $y = 5e^{(x/5)-1}$ for $0 \leq x \leq 5$, and $y = x$ for $5 \leq x \leq 10$? – Brian Tung Apr 19 '15 at 05:57
  • @BrianTung isn't possible to have these two behaviour in one equation. – user2293224 Apr 19 '15 at 06:00
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    Why does it have to be in one equation? If you're waiting for our valuable suggestions, it would help if we knew what the context was. – Brian Tung Apr 19 '15 at 06:01
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    Hi, user2293224 ! Your question is ambiguous because many different answers can be given, depending on the context of the problem. Without more information and without knowing the context, one can give an equation which will disappoint you. For example, the piecewise function defined above by Brian Turing $y=5e^{(x/5)-1}$ for $0\leq x\leq 5$, and $y=x$ for $5\leq x\leq 10$, can be written on the form of one equation only : $y=5e^{(x/5)-1}H(5-x)+x H(x-5)$ where $H(x)$ is the Heaviside function. – JJacquelin Apr 19 '15 at 07:24
  • @JJacquelin sorry for the ambiguity. Actually i am looking for continuous function that can take any number in between 0 to 10 and gives the aforementioned behavior. As i want to show this behavior in one line (or curve) in graph that's why I thought to have in one equation. The context is i am looking to generate a behavior where the population growth is exponential around in the middle of x-axis and later on it convert to linear nature. Hope this explanation remove some confusion. – user2293224 Apr 19 '15 at 09:00
  • @BrainTung please read my recent comment. hopefully it helps you in understanding my context. – user2293224 Apr 19 '15 at 09:02
  • @user2293224 : The question is not yet specific enough to give a pertinent answer. For example, I suggest to have a look at the logistic equation (or some equations of similar kind) http://mathworld.wolfram.com/LogisticEquation.html – JJacquelin Apr 19 '15 at 09:37

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