11.1 Problem9

I arrived at the right answer however I have no idea why those are the
right answers. Can you go through the steps to solve this?

Each level curve is the solution of an equation  f(x,y)=A,B,C,D.  The curve for f(x,y)=A is the easiest, because it *looks* like A must be equal f(0,0)=140e^0-70*0^2=140, and this is a multiple of 10.  For f(x,y)=B the problem is a little more complicated--it looks like f(x,0)=B for an x close to 0.4--and we need B to be an integer multiple of 10. Since y=0 on the x-axis and increasing values of x mean increasing values of f, it looks like B must be equal to 140e^0.4, but this is equal to 208.86 which is not a multiple of 10.  The nearest multiple of 10, though is 210, which means that x=ln(210/140)=0.405, which is close enough to what we see