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Figure 1

Given information : Figure shows contours of f(x,y)=140ex−50y2.

The question is: Find the values of $f$ on the contours. They are equally spaced multiples of 10.

I am having a little trouble understanding what "equally spaced multiples of 10" means.
Based on my understanding, I know that I have to calculate $z$, so I first found $z$ for each curve.

\begin{align} z &= f(0,0) = 140\exp(0)-0 = 140. \\ \text{Similarily,}\quad z &= f(0.4,0) = 140\exp(0.4), \\ z &= f(0.7,0) = 140\exp(0.7), \\ z &= f(0.9,0) = 140\exp(0.9). \end{align}
I plugged in these values for Curves $A,B,C,D$, but it is incorrect. I am not really sure if the information "equally spaced multiples of 10" is affecting my answer of if I am missing something else...

g.kov
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h.jb
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1 Answers1

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enter image description here

Equally spaced multiples of 10

means that every $z$-values on every line has constant difference with a neighbour line, and this difference can be $10,20,30,\dots$

The confusion comes due to not very accurate graph. If we use, for example, \begin{align} f(0,0)&= 140 ,\\ f(0.408,0)&\approx 210 ,\\ f(0.695,0)&\approx 280 ,\\ f(0.917,0)&\approx 350 . \end{align}

Then it is clear that the $z$-step in contour lines here is $70$, starting with $z=140$.

g.kov
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