Exponential simultaneous equation with powers

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In summary, the problem is to solve for r in the equation (e^(r-0.04)^(5/12))(0.9463) = (e^(r-0.04)^(11/12))(0.95152). By taking the natural log of both sides and using the property of exponents, the solution is r~2.90%.
  • #1
acu04348
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Hi there,Struggling with this problem, anyone know how this might be solved?

(e^(r-0.04)^(5/12))(0.9463) = (e^(r-0.04)^(11/12))(0.95152)

and solve for r

Ans: r~2.90%

Would really appreciate it!
 
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  • #2
acu04348 said:
Hi there,Struggling with this problem, anyone know how this might be solved?

(e^(r-0.04)^(5/12))(0.9463) = (e^(r-0.04)^(11/12))(0.95152)

and solve for r

Ans: r~2.90%

Would really appreciate it!
It's hard to tell for certain what you're working with. Is this it?
[tex]0.9463(e^{r - .04})^{5/12} = .95152(e^{r - .04})^{11/12}[/tex]

If so, when you raise an exponent to a power, the exponents multiply, so the above can be rewritten as
[tex]0.9463e^{(5/12)(r - .04)} = .95152e^{(11/12)(r - .04)}[/tex]

Now take the natural log of both sides.
 
  • #3
Thank you Mark44.
 

1. What is an exponential simultaneous equation with powers?

An exponential simultaneous equation with powers is a set of equations that involve variables raised to different powers. These equations are solved simultaneously, meaning the values of the variables satisfy all of the equations at the same time.

2. How is an exponential simultaneous equation with powers different from a regular simultaneous equation?

An exponential simultaneous equation with powers differs from a regular simultaneous equation in that the variables are raised to different powers, rather than being linearly related. This means that the equations may have multiple solutions or no solutions at all.

3. What is the general method for solving an exponential simultaneous equation with powers?

The general method for solving an exponential simultaneous equation with powers is to isolate one of the variables in one of the equations and substitute it into the other equations. This process is repeated until all the equations have been simplified to a single variable equation, which can then be solved for the variable. The obtained value is then substituted back into the other equations to find the values of the remaining variables.

4. Can an exponential simultaneous equation with powers have infinite solutions?

Yes, an exponential simultaneous equation with powers can have infinite solutions. This occurs when the equations are equivalent, meaning they are just different representations of the same relationship. In this case, any value for the variables that satisfies one equation will also satisfy the others.

5. Are there any practical applications of exponential simultaneous equations with powers?

Yes, exponential simultaneous equations with powers are commonly used in fields such as physics, engineering, and finance to model complex relationships between variables. They can also be used to solve problems involving growth or decay, such as population growth or radioactive decay.

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