How could I make an exponential function which has a limit of around 1.53?

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This discussion focuses on modeling a variable output Y that approaches a limit of approximately 1.53 as x increases. The proposed function is y = 1.53 - 0.53/(a*x+1), where a is a non-negative parameter that controls the rate of approach to the limit. The discussion emphasizes adjusting the value of a to determine specific output values, such as y reaching 1.35 at a defined x. This approach effectively captures the behavior of Y as it increases at an exponentially decreasing rate.

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I'm modelling a variable output Y which has a value of 1 at x=0.

I've noticed that in the system I'm modelling, as x increases, y increases at an exponentially decreasing rate, up until a limit of around 1.53. I view this as changes in x causing the Y value to increase by a max of 53%.

The only problem is I've been working at it but I don't know where to begin in modelling a function with such a limit.

Can anyone think of a solution?

Thanks!
 
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You could use something like y = 1.53 - 0.53/(a*x+1), where a >= 0. I'm assuming x >= 0 as well here.

Adjust a to determine how quickly it approaches 1.53, for example determine the x at which y is say 1.35 (2/3rds), in which case a = 2/x.
 
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Lord Crc said:
You could use something like y = 1.53 - 0.53/(a*x+1), where a >= 0. I'm assuming x >= 0 as well here.

Adjust a to determine how quickly it approaches 1.53, for example determine the x at which y is say 1.35 (2/3rds), in which case a = 2/x.

Good solution, Thanks!
 

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