In this graph, the blue line is 'inner' and the red one is 'outer'. I want to make inner/outer to have maximum value near $x = 40$ to $50$. However, just dividing inner by outer is not good. So I want to manipulate 'outer' using some functions, such as exponential and logarithm and make right-side values of 'outer' to increase, which is currently steady state. In this way, I can get inner/(manipulated outer) to have maximum near $x = 40$ to $50$. I've tried exponential(outer) and logarithm(outer), but it still has minimum near $x = 10$.
please share your opinion

You can add a line to outer. It would appear you need the line to pass through points roughly (100,0) and (350,0.05), which gives you a slope of $0.05/250=2\times10^{-4}$. The equation for such a line is $y=2\times10^{-4}x-2\times10^{-2}$