Given:
The graph of an exponential function.
To find:
The function in the form of [tex]f(x)=ab^x[/tex].
Solution:
The general form of an exponential function is
[tex]f(x)=ab^x[/tex] ...(i)
From the given graph it is clear that the function passes through the points (0,4) and (1,7). It means these points will satisfy the function.
For x=0 and f(x)=4,
[tex]4=ab^0[/tex]
[tex]4=a(1)[/tex]
[tex]4=a[/tex]
For x=1 and f(x)=7,
[tex]7=ab^1[/tex]
Putting a=4, we get
[tex]7=4(b)[/tex]
[tex]\dfrac{7}{4}=b[/tex]
Substitute a=4 and [tex]b=\dfrac{7}{4}[/tex] in (i).
[tex]f(x)=4\left(\dfrac{7}{4}\right)^x[/tex]
Therefore, the required exponential function is [tex]f(x)=4\left(\dfrac{7}{4}\right)^x[/tex].
