need to linearize r=u(1-exp(s/k))*c where some combination of r, s, and c is the independent variable, s or c is the dependent variable, and u and k must be involved in the parameters of the linearization
To linearize the equation r = u(1 - exp(s/k)) * c, we need to express the given equation in a linear form by manipulating the variables and parameters.
Step 1: Identify the independent and dependent variables.
In this equation, r, s, and c are the variables. To linearize the equation, we need to choose one of these variables as the independent variable and express the others in terms of it. Let's choose s as the independent variable.
Step 2: Express r and c in terms of s.
To express r and c in terms of s, rearrange the equation as follows:
r = u(1 - exp(s/k)) * c
Divide both sides by c to isolate r:
r/c = u(1 - exp(s/k))
To express c in terms of s, rearrange the equation again:
c = (r/u) / (1 - exp(s/k))
Step 3: Linearize the equation.
Now, we have r/c = u(1 - exp(s/k)) and c = (r/u) / (1 - exp(s/k)).
To linearize the equation, we will introduce new variables and parameters. Let's define the following constants: A = r/u and B = 1/k.
Rearranging both equations using the new variables, we get:
r/c = A(1 - exp(sB))
Notice that by choosing A and B appropriately, we can make r/c the dependent variable while s becomes the independent variable. Therefore, we have successfully linearized the equation.
In summary, to linearize the equation r = u(1 - exp(s/k)) * c:
1. Define new constants: A = r/u and B = 1/k.
2. Express r and c in terms of s: r/c = A(1 - exp(sB)).
3. The dependent variable is r/c while s is the independent variable, and the parameters u and k are involved in the linearization through A and B.