How Can You Modify an Equation to Favor a Specific Variable Value?

[clydas]

Suppose I have the following equation:
P=a*n
Where a is a value between 0 and 1.
n is the day of the week. (this is just an example)

How do I change this expression so, for example, if one were to put 5 for n, the result would be marginally greater than those resulting from inserting any other number (1,2,3,4,6,7)?
Common sense dictates putting in (n/5), but that does not work if one inputs 6 or 7 into the equation.

Enlightenment on the area of math that such processes deal with would be great help as well.

 

[micromass]

Hi clydas!

I'm not sure what you want to do with this, so I don't know if you will like the answer.

The trick is to change n with a function that takes a maximum in 5. For example

$$P=a*(-(n-5)^2)$$

Or

$$P=a*(-(n-5)^2+100)$$

Or even

$$P=a*e^{-(n-5)^2}$$

 

[clydas]

Hi clydas!

I'm not sure what you want to do with this, so I don't know if you will like the answer.

The trick is to change n with a function that takes a maximum in 5. For example

$$P=a*(-(n-5)^2)$$

Or

$$P=a*(-(n-5)^2+100)$$

Or even

$$P=a*e^{-(n-5)^2}$$

Ah, now it seems obvious.

Thank you very much! Your answer is perfect!
Just for the record: I'm not that slow in math as it might appear, it's just that sometimes the most obvious of things are the least noticeable.

Thanks again!