Apps. and Interpretation for IBDP Maths Ebook 1 | Page 45

11
Paper 1 – Exponential Functions
Example
The function f( x ) is defined as f ( x) �13� a� 2 bx , where b � 0 . The graph of f( x )
intersects the y -axis at (0,19) .
(a) Find the value of a .
The graph of f( x ) passes through (1,13.75) .
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(b) Find the value of b .
(c) Write down the equation of the horizontal asymptote of the graph of f( x ).
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Solution
(a)
(b)
19 �13� a� 2 b(0)
(M1) for substitution
19 �13�
a
a � 6
A1 N2
13.75 �13� 6� 2 b(1)
(M1) for substitution
b
0.75 �6�2 � 0
By considering the graph of y � 0.75 �6� 2 b ,
b �� 3 . A1 N2
(c) y � 13
A2 N2
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