0606 P12 - Mar 2018 - Q9 - 11 marks
8394
Variables \(x\) and \(y\) are connected by the equation \(y=Ae^{bx}\), where \(A\) and \(b\) are constants. The table shows corresponding values of \(x\) and \(y\).
| \(x\) | 2 | 4 | 6 | 8 | 10 |
|---|---|---|---|---|---|
| \(y\) | 736 | 271 | 100 | 37 | 13 |
(i) Transform the equation \(y=Ae^{bx}\) into the equation of a straight line.
(ii) Use a suitable graph to show that \(x\) and \(y\) are connected by the equation \(y=Ae^{bx}\).
(iii) Use your graph to estimate the values of \(A\) and \(b\).
(iv) Estimate the value of \(x\) when \(y=500\).
(v) Estimate the value of \(y\) when \(x=5\).
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