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Graph of a^x

The diagram shows a sketch of the graph y=ab^x.
The curve passes through the points A(1/3, 1/2) and B(2, 16).
The point C(-1/3, k) lies on the curve.
Find the value of k.

Can someone please show me and explain to me how to do this as I've been trying for the last half an hour, thanks.
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Original post by Dungey95
The diagram shows a sketch of the graph y=ab^x.
The curve passes through the points A(1/3, 1/2) and B(2, 16).
The point C(-1/3, k) lies on the curve.
Find the value of k.

Can someone please show me and explain to me how to do this as I've been trying for the last half an hour, thanks.


y=abx y = ab^x

Sub in (13, 12) \left(\dfrac13, \ \dfrac12 \right)

This gives, 12=ab13(1) \displaystyle \frac12 = ab^{\frac13} \longrightarrow (1)

Sub in (2, 16) \left( 2, \ 16 \right)

16=ab2(2) 16 = ab^2 \longrightarrow (2)

Find (2)÷(1) (2) \div (1) , you will see a a cancels out.

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