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

In summary, the conversation discusses the process of modelling a variable output Y with a value of 1 at x=0 and how it increases at an exponentially decreasing rate until reaching a limit of around 1.53. The speaker is struggling to find a way to model a function with such a limit and asks for suggestions. A possible solution is proposed, using the formula y = 1.53 - 0.53/(a*x+1), with a value of 0 or greater, and adjusting a to determine how quickly it approaches 1.53. The x value can also be adjusted to determine the desired y value, with a being equal to 2/x in this case.
  • #1
mpatryluk
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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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  • #2
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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  • #3
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!
 

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

1. How do I determine the base value for my exponential function?

The base value of an exponential function is the number that is raised to a power. In order for your function to have a limit of 1.53, you will need to choose a base value that is less than 1, but greater than 0. This will result in an exponential decay function, approaching 1.53 as the input values increase.

2. Can I use any number for the rate of change in my exponential function?

No, the rate of change, also known as the growth or decay factor, must be positive in order for the function to be an exponential. In this case, since the limit is less than 1, the rate of change must be less than 1 as well.

3. How do I find the value of the limit for my function?

To find the limit of an exponential function, you can simply plug in a large number for the input value. As the input approaches infinity, the output will approach the limit value of 1.53. You can also use mathematical techniques such as L'Hopital's rule to find the limit analytically.

4. Can I use a negative number for the limit of my exponential function?

Yes, you can use a negative number for the limit of your exponential function. This will result in an exponential growth function, approaching the negative limit value as the input values increase.

5. How can I make sure my exponential function does not exceed the limit of 1.53?

In order to ensure that your exponential function has a limit of 1.53, you will need to carefully choose the base value and rate of change. As mentioned before, the base value should be less than 1 and the rate of change should be positive and less than 1. You can also use a graphing calculator to visually confirm that your function stays below the limit value.

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