Finding a wrong reading in exponential data
Finding a wrong reading in exponential data
IP 3
8 marks
The variables \(x\) and \(y\) are believed to satisfy \(y=ab^x\), where \(a\) and \(b\) are positive constants. One of the readings of \(y\) below was recorded incorrectly.
| \(x\) | \(0\) | \(1\) | \(2\) | \(3\) | \(4\) |
|---|---|---|---|---|---|
| \(y\) | \(3\) | \(6\) | \(12\) | \(20\) | \(48\) |
- Explain why, if \(y=ab^x\), the graph of \(\lg y\) against \(x\) is a straight line and the ratio of each reading of \(y\) to the previous one is constant.[3]
- Without drawing a graph, identify the incorrect reading and state its correct value.[3]
- Find \(a\) and \(b\), and predict \(y\) when \(x=6\).[2]
Solution:
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Answer:(b) \(y=20\) at \(x=3\) should be \(24\) (c) \(a=3,\ b=2\); \(y=192\)
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