Moderate -0.8 This is a straightforward substitution problem requiring students to form two simultaneous equations from given points and solve for two unknowns. It tests basic understanding of exponential functions but involves only routine algebraic manipulation with no conceptual challenges or problem-solving insight required.
\(\log 6 = \log a + \log b\) and \(\log 3.6 = \log a + \log b^2\)
\(a = 10, b = 0.6\) c.a.o.
A2
A1 each; if M0 then B3 for both, B1 for one
$6 = ab$ and $3.6 = ab^2$ | M1 | $\log 6 = \log a + \log b$ and $\log 3.6 = \log a + \log b^2$
$a = 10, b = 0.6$ c.a.o. | A2 | A1 each; if M0 then B3 for both, B1 for one
4 The graph of $y = a b ^ { x }$ passes through the points $( 1,6 )$ and $( 2,3.6 )$. Find the values of $a$ and $b$.
\hfill \mbox{\textit{OCR MEI C2 2011 Q4 [3]}}