3.74: Linear law: ln⁡y\ln y against x2x^{2} for y=Abx2y=Ab^{x^{2}}

0606/13/O/N/24 — Question 6 · 9 marks

(a)
The table shows x,yx,y related by y=Abx2y=Ab^{x^{2}}.
| xx | 11 | 1.51.5 | 22 | 2.52.5 | 33 |
| yy | 1414 | 33.333.3 | 112112 | 532.8532.8 | 35843584 |
Draw a straight line graph of ln⁡y\ln y against x2x^{2}.
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(b)
Estimate AA and bb correct to 11 significant figure.
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(c)
Estimate xx when y=200y=200, correct to 22 significant figures.
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