However, while dollar cost to move between classes of service is exponential [1] the number of points required is approximately logarithmic [2].<p>Even using American&#x27;s post-devaluation chart (one-way):<p>* economy 35,000<p>* business 70,000<p>* first 90,000<p>So, buy miles when on sale, fly first at a significant discount subject to availability.<p>[1] <a href="https:&#x2F;&#x2F;www.wolframalpha.com&#x2F;input&#x2F;?i=quadratic+fit+%7B1,900%7D,%7B2,2000%7D,%7B3,6000%7D,%7B4.0,10000%7D" rel="nofollow">https:&#x2F;&#x2F;www.wolframalpha.com&#x2F;input&#x2F;?i=quadratic+fit+%7B1,900...</a>
[2] <a href="https:&#x2F;&#x2F;www.wolframalpha.com&#x2F;input&#x2F;?i=log+fit+%7B1,35000%7D+%7B3,+70000%7D,+%7B4,+90000%7D" rel="nofollow">https:&#x2F;&#x2F;www.wolframalpha.com&#x2F;input&#x2F;?i=log+fit+%7B1,35000%7D+...</a>