Sketching the line for a natural exponential law
Sketching the line for a natural exponential law
Secondary 3
The variables \(x\) and \(y\) are related by \(y=8\mathrm{e}^{-0.5x}\).
- Sketch the graph of \(\ln y\) against \(x\), marking where it meets both axes and stating its gradient.
- Use your line to find the value of \(x\) for which \(y=1\), and explain why the line crosses the horizontal axis there.
Solution:
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Answer:(a) line through \((0,\,2.08)\) and \((4.16,\,0)\), gradient \(-0.5\) (b) \(x=2\ln 8\approx4.16\), because \(\ln 1=0\)
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