Respuesta :
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
[tex]y=ab^x[/tex] ...(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).
[tex]y=8b^x[/tex] ...(ii)
It contains the point (3,64). Put x=3 and y=64.
[tex]64=8b^3[/tex]
Divide both sides by 8.
[tex]\dfrac{64}{8}=b^3[/tex]
[tex]8=b^3[/tex]
[tex]2^3=b^3[/tex]
On comparing both sides, we get
[tex]b=2[/tex]
Put b=2 in (ii).
[tex]y=8(2)^x[/tex]
The functions form of this equation is
[tex]f(x)=8(2)^x[/tex]
Therefore, the required function is [tex]f(x)=8(2)^x[/tex].
