Sketching the line for an exponential law

Sketching the line for an exponential law

Secondary 3

The variables \(x\) and \(y\) are related by \(y=0.2(5^x)\).

  1. Show that the graph of \(\lg y\) against \(x\) is a straight line, and state its gradient and vertical intercept.
  2. Sketch the line, marking where it meets both axes.
  3. The point \((2,\,k)\) lies on the line. Find \(k\) and the corresponding value of \(y\).
  4. State the gradient and the vertical intercept of the line obtained if \(\ln y\) is plotted against \(x\) instead.

Solution:

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Answer:(a) gradient \(\lg 5\approx0.699\), intercept \(-\lg 5\approx-0.699\) (b) line through \((0,\,-0.699)\) and \((1,\,0)\) (c) \(k=\lg 5\approx0.699\), \(y=5\) (d) gradient \(\ln 5\approx1.61\), intercept \(\ln 0.2\approx-1.61\)

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