Is that Function Homogeneous

[know]

Examine the homogeneity of the function:
F(a,b,c)=200a²*√c * e^(0.01b)
I tried to find the solution but I don't understand how to treat the "e^0.01b"
the part I completely don't understand is that "b"
Can anyone explain me how to get the result?

 

[Steven G]

Please show us your work.

 

[Dr.Peterson]

Examine the homogeneity of the function:
F(a,b,c)=200a²*√c * e^(0.01b)
I tried to find the solution but I don't understand how to treat the "e^0.01b"
the part I completely don't understand is that "b"
Can anyone explain me how to get the result?

We will need to see what you've done; but you may just need to consider the fact that [MATH]\left(a^m\right)^n = a^{mn}[/MATH].

 

[know]

F( λa , λb, λc)= 200* λ²*a²* √ λc * e ^{(0.01 λ b)}

 

[Dr.Peterson]

F( λa , λb, λc)= 200* λ²*a²* √ λc * e ^{(0.01 λ b)}

Good (though you should use parentheses, √(λc), to clarify).

Now apply the rule I suggested! If you don't see why, tell us what your goal is at this point.

 

[know]

I need to find the value of λ ^α from that formula:
f(λx1, λx2, . . . , λxn) = λ ^α f(x1, x2, . . . , xn).
But I don't understand how?

 

[Dr.Peterson]

Well, the problem says,

Examine the homogeneity of the function:
F(a,b,c)=200a²*√c * e^(0.01b)

As I read it, that doesn't mean, "Show that it is homogeneous", but rather, "Determine whether it is homogeneous, and support your conclusion". So if you're having trouble, maybe it isn't ...

 

[know]

I need to find the value of λ ^α from that formula:
f(λx1, λx2, . . . , λxn) = λ ^α f(x1, x2, . . . , xn).
But I don't understand how?

Is there any way to get result and how?

 

[Dr.Peterson]

Is there any way to get result and how?

Let's look at what you've done so far:

F( λa , λb, λc)= 200* λ²*a²* √(λc) * e ^{(0.01 λ b)}

We can apply the rule I've mentioned in an attempt to get λ on the outside of the exponential, and also split up the radical similarly:

200 λ² a² √λ √c (e ^{(0.01 b)})^λ

But as you are presumably observing, that last λ is not multiplying the rest of the formula, and it doesn't look like you can do any better.

So what do you do if it doesn't look like what you want to prove is true? You try to prove that it is not true! The ultimate goal is proof, not the truth of the claim, in the sense that you want to prove something, one way or the other.

To prove a claim is not true, you look for a counterexample. Try some numbers for a, b, c, and λ, and see if it turns out that f(λa, λb, λc) = λ α f(a, b, c). If not, you have proved the claim is false, and that is a victory!