Fitting a curve - trending line formula

Question

In OSX Numbers I have a chart with these data points:

50  53
100 62
200 78
300 91
500 117
1000 192
2000 297
3000 412
5000 567
10000 990

Using the trending line option I see that an exponential formula works well and is given as:

35.907e^(0.3498x)

However when I run this formula using Y values I get nowhere near X. With 50 I get something like 1.5 billion for X.

I am a little rusty on my math so perhaps interpreting it wrong. Is this formula a correct approximation?

Answer 1

As mfl commented, a linear fit $y=a+bx$ looks more appropriate than $y=ae^{bx}$.

For the linear model, as already given by mfl, we should get $$y=76.6228+0.0944818 x\qquad SSQ=7363.8\qquad R^2=0.995485$$

Because of the curvature for low values of $x$, a better fit could be obtained using $y=a+bx^c$. For such a case $$y=37.6705+0.57678 x^{0.804092}\qquad SSQ=485.984\qquad R^2=0.999702$$ which is definitively much better.