For this question it does to the power of x. I remember from unit 1 spec that this is a geometric sequence, but that's the only reason I know how they got the answer. Is there a more intuitive way to think about this relationship?

Thank You!

I can see how one can draw connections to geometric sequences - well done.

Indeed, this is a bit of a weird question. I don't really have a great way of explaining this intuitively, so perhaps someone else could post their ideas, but I'll give it a shot.

First, let's ignore the fact that they butchered the question wording. \(0.92^{1/10}<1\), so to decrease the area by this factor as \(x\) increases actually increases the area lol.

Let's think about it this way. For every meter further from \(B\), you need to multiply by that factor of \(0.92^{1/10}\). For example: \[\text{At }x=1 \text{ m},\ \ A=0.02\times (0.92^{1/10})^1\ \text{mm}^2\\

\text{At }x=2 \text{ m},\ \ A=0.02\times(0.92^{1/10})^2\ \text{mm}^2\\

\text{At }x=1/2 \text{ m},\ \ A=0.02\times(0.92^{1/10})^{1/2}\ \text{mm}^2,\] and so drawing out this idea, at \(x\) metres, you must multiply by the factor \(0.92^{1/10}\) '\(x\) times': \[A(x)=0.02\times (0.92^{1/10})^x=0.02\times 0.92^{x/10}\]