# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#3

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**Question**

The variables x and y satisfy the equation y = A(b^{-x)}, where A and b are constants. The graph of ln y against ln x is a straight line passing through the points (0, 1.3) and (1.6, 0.9), as shown in the diagram. Find the values of A and b, correct to 2 decimal places.

** Solution**

We are given;

Taking natural logarithm of both sides;

Multiplication Rule;

Power Rule;

Slope-Intercept form of the equation of the line;

Where is the slope of the line.

Comparing the standard equation with above obtained equation, it is evident that it is equation of a straight line and;

We are given that a straight line passing through the points (0, 1.3) and (1.6, 0.9) is line of graph against .

We can find slope of this line to equate with slope of line whose equation is obtained above.

Expression for slope of a line joining points and ;

Therefore;

Taking anti-logarithm of both sides;

for any

Similarly we can equate the y-intercepts of given line (0,1.3) and obtained equation of line.

The point at which curve (or line) intercepts y-axis, the value of .

Therefore;

Taking anti-logarithm of both sides;

for any

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