Homework question. Extra. MAPS

[Speedy232]

Homework Statement

Composers often use a "fade out" at the end of a song.
Sound Engineers then have to choose a mathematical function (called damp functions) which makes the fade sound natural. The simplest choice is a linear function but, for most people, this function makes the sound fade too quickly at the beginning of the fade out. The most natural sounding fade is a logarithmic function.

Use your knowledge of transformations to find a suitable model of this function. You must justify your solution by stating your initial 'starting' function and then demonstrating and explaining how the function is changed by each of the constant values you introduce and/or change. Modify your model as needed in order to be sure that it is consistent with the problem posed.

Demonstrate and explain clearly a method to validate your model so that you can be sure that it is correct, including domain restrictions

On the y-axis it goes up in 0.1 which is called the amplitude. The x-axis goes up in 0.5 which is called time. You can just see the line. But from here, i don't know what to do? please help. Any help would be really appreciated.

Homework Equations

All i know is that log limits may apply to changing or making this graph.

The Attempt at a Solution

 

[Дьявол]

Hint: f(x)=ln(-ax+y)+z

where a,y,z>0 and a,y,z are constants.

Now judge by the intersection points and you will find the solution.

Regards.

 

[Speedy232]

That is quite helpful. Thank you. But what formula is that called. I can't see it anywhere in my textbook, and they expect us to know that, to solve that, and what's this + Z, I've never heard of a formula that uses that.

 

[Дьявол]

Could you possibly tell me, concretely what functions, transformations, operations etc you should use to solve the tasK?

Anyway, I will explain you. by increasing 'z' the amplitude of the graph is increasing, i.e the graph is top shifted (if z>0) or bottom shifted (if z<0).

By increasing 'y' the graph is right shifted (if y>0) and left shifted (if y<0)

$$ln$$ is $$log_e$$

 

[Speedy232]

We are allowed to use any transformations we want. We just have to find out how that graph was made then by finding that equation, put it in our graphics calculator and then show it to our teacher. Thats all. Its proving harder than thought.

 

[Speedy232]

Theres another example in my book that has the formula of y= A ln (x + B) + c

But the answer they have is ln(x+1)+1. Which seems to be the opposite of my graph or close enough to the one I am looking out. Any more help?

 

[Дьявол]

Theres another example in my book that has the formula of y= A ln (x + B) + c

But the answer they have is ln(x+1)+1. Which seems to be the opposite of my graph or close enough to the one I am looking out. Any more help?

Ok, and can you please give me another screen shot. This picture is very blur and I can't see the graph correctly.

Regards.