The variables $$\(x\)$$ and $$\(y\)$$ satisfy the equation $$\(x=A\left(3^{-y}\right)\)$$, where $$\(A\)$$ is a constant. Explain why the graph of $$\(y\)$$ against $$\(\ln x\)$$ is a straight line and state the exact value of the gradient of the line. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_32 Year：2021 Question No：3(a)
Answer:
State or imply \(\ln x=\ln A-y \ln 3\)
State that the graph of \(y\) against \(\ln x\) has an equation that is linear in \(y\) and \(\ln x\),
or has an equation of the standard form ' \(y=m x+c\) ' and is thus a straight line
State that the gradient is \(-\frac{1}{\ln 3}\)
State that the graph of \(y\) against \(\ln x\) has an equation that is linear in \(y\) and \(\ln x\),
or has an equation of the standard form ' \(y=m x+c\) ' and is thus a straight line
State that the gradient is \(-\frac{1}{\ln 3}\)
Knowledge points:
3.2.4 use logarithms to transform a given relationship to linear form, and hence determine unknown constants by considering the gradient and/or intercept.
Solution:
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