Logarithm function from graph (word problem)

Question

I was hoping to find some hint to solve this:

There is an internet company that wants to price their service $30/month, which will include 25GB on their package. After 25GB, the price will increase logarithmically until 60 dollars for 60GB

I know the Y axis would be price and X axis would be the GB..

Two known point is (25, 30) which is starting price and monthly allowance of GB, and (60, 60). There is a logarithmic curve between those two points. How do I find the equation for this? It is supposed to be in the form of f(x) = a + b ln |x|

Answer 1

You need to define a piecewise function K(u) where u is the data usage in GB such that:

         { 25       | u<=25;    }
    K(u)={ 25+f(u)  | 25<u<=60; }
         { 60       | u>60      }

Here, f(u) is the function that you need to find; i.e. y(x)=a + b ln(x)
Then you would solve for b the following equations:

    (1) y1=b*ln(x1)
    (2) y2=b*ln(x2)

From there it's just a matter of plugging and chugging to evaluate for b.