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Given:
Y-intercept of exponential function is 8.
It contains the point (3,64).
To find:
The exponential function that describes the graph.
Solution:
The general form of an exponential function is
...(i)
where, a is initial value or y-intercept and b is growth factor.
Since, y-intercept is 8, therefore, a=8.
Put a=8 in (i).
...(ii)
It contains the point (3,64). Put x=3 and y=64.
Divide both sides by 8.
On comparing both sides, we get
Put b=2 in (ii).
The functions form of this equation is
Therefore, the required function is .