1 of 8 0-day streak

Logarithmic data transformations

Question 1 of 8

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The table gives explanatory values \(x\) and response values \(y\)

\(x\)	\(10\)	\(1000\)	\(100000\)	\(100000000\)
\(y\)	\(\frac{14}{3}\)	\(42\)	\(\frac{350}{3}\)	\(\frac{896}{3}\)

(a)3 marks

Find the missing entries in the transformed x-row

\(x\)	\(10\)	\(1000\)	\(100000\)	\(100000000\)
\(y\)	\(\frac{14}{3}\)	\(42\)	\(\frac{350}{3}\)	\(\frac{896}{3}\)
\(\log_{10}(x)\)	?	3	?	?

\(\log_{10}(x)\) when x = 10 \(\log_{10}(x)\) when x = 100000 \(\log_{10}(x)\) when x = 100000000

(b)1 mark

Are all successive slopes in the transformed coordinates equal?

Yes. All successive transformed slopes are equal

No. The successive transformed slopes are not all equal