A-LevelMathematicsLogarithmic and exponential functions9709/22 · Feb/Mar 2019 · Q35 Marks
The variables x and y satisfy the equation y = AePx+P, where A and p are constants. The graph of ln y against x is a straight line passing through the points (1, 2.835) and (6, 6.585), as shown in the diagram. Find the values of A and p. [Figure X.X]
- The variables x and y satisfy the equation y = AePx+P, where A and p are constants. The graph of ln y against x is a straight line passing through the points (1, 2.835) and (6, 6.585), as shown in the diagram. Find the values of A and p.[5]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [B1] State or imply equation is ln y = ln A + px + p
- [M1] Equate gradient of line to p
- [A1] Obtain p = 0.75
- [M1] Substitute appropriate values to find ln A
- [A1] Obtain ln A = 1.335… and hence A = 3.8
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