The variables $$$x$$$ and $$$y$$$ satisfy the equation $$$y=A x^{-2 p}$$$, where $$$A$$$ and $$$p$$$ are constants. The graph of $$$\ln y$$$ against $$$\ln x$$$ is a straight line passing through the points $$$(-0.68,3.02)$$$ and $$$(1.07,-1.53)$$$, as shown in the diagram. Find the values of $$$A$$$ and $$$p$$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_22 Year：2020 Question No：4

Answer:

State or imply equation is $\ln y=\ln A-2 p \ln x$
Equate gradient of line to $-2 p$
Obtain $-2 p=-2.6$ and hence $p=1.3$
Substitute appropriate values to find $\ln A$
Obtain $\ln A=1.252$ and hence $A=3.5$
Alternative method for question 4
State or imply equation is $\ln y=\ln A-2 p \ln x$
Substitute given coordinates to obtain 2 simultaneous equations and solve to obtain $3.5 \mathrm{p}$
Obtain $3.5 p=4.55$ and hence $p=1.3$
Substitute appropriate values to find $\ln A$
Obtain $\ln A=1.252$ and hence $A=3.5$

Knowledge points:

2.2.4 use logarithms to transform a given relationship to linear form, and hence determine unknown constants by considering the gradient and/or intercept.

Answer:

Knowledge points:

Solution:

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