Solve y=1- A(1-e^(-kx)) + mx +b

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In summary: There may be more than one solution, but you can find a good enough approximation if you need one.)Iterate this process until you have a good solution.
  • #1
O_chemist
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At work today one of the biologist came and asked me with help on solving a problem. I need a little hint as I still would like to solve this problem.

y=1- A(1-e^(-kx)) + mx +b

A, k, m and b are all constants

I need to solve for x but it results in getting a -kx-ln(x) = some junk
From what I can see there isn't a way to do this analytically as I will go in an endless cycle of e's and ln's. I did some research about using iterative method for solving this. What I want to know is from people who do this more often is there a more simple method I could use? Just give me a hint ;) .

Regards,
Caleb
 
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  • #2
O_chemist said:
At work today one of the biologist came and asked me with help on solving a problem. I need a little hint as I still would like to solve this problem.

y=1- A(1-e^(-kx)) + mx +b

A, k, m and b are all constants

I need to solve for x but it results in getting a -kx-ln(x) = some junk
From what I can see there isn't a way to do this analytically as I will go in an endless cycle of e's and ln's. I did some research about using iterative method for solving this. What I want to know is from people who do this more often is there a more simple method I could use? Just give me a hint ;) .
There's the Lambert W function, https://en.wikipedia.org/wiki/Lambert_W_function, but the way I would approach it would be as a numerical solution.
Your equation is equivalent to ##1 - A(1 - e^{-kx}) + mx + b - y = 0##, with A, k, m, and b known constants, and the value for y known.

Pick a value for x, and plug it in. Is the result zero? Probably not, but if so, you've found the solution.
If not, pick a different value for x, and evaluate the expression. Choose values for x that make the expression on the left side as close to zero as you can.
 

Related to Solve y=1- A(1-e^(-kx)) + mx +b

1. How do I solve for the value of y?

The equation y=1- A(1-e^(-kx)) + mx +b is already solved for y. It is not necessary to solve for y as it is the dependent variable in the equation.

2. What do the variables A, k, m, and b represent?

A, k, m, and b are all constants in the equation. A represents the amplitude, k represents the rate of decay, m represents the slope, and b represents the y-intercept.

3. Can I solve this equation without knowing the values of A, k, m, and b?

No, in order to solve this equation, you will need to know the values of A, k, m, and b.

4. How do I graph this equation?

This equation can be graphed by plotting points on a coordinate plane. Choose values for x and solve for y to get the coordinates. Then, plot the points and connect them with a smooth curve.

5. Can I use this equation to model real-world situations?

Yes, this equation can be used to model various real-world situations, such as population growth or decay, financial investments, and chemical reactions.

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