Answer:
The correct option is 4.
Step-by-step explanation:
It is given that the table represents an exponential function.
Let the exponential function is
[tex]f(x)=ab^x[/tex]
From the table it is noticed that the function passing through the points (2,25), (3,125) and (4,625). It means the function must be satisfied by the points.
[tex]25=ab^2[/tex] .... (1)
[tex]125=ab^3[/tex] ..... (2)
Divide equation 2 by equation 1.
[tex]\frac{125}{25}=\frac{ab^3}{ab^2}[/tex]
[tex]5=b[/tex]
The value of b is 5. Put this value in equation (1).
[tex]25=a(5)^2[/tex]
[tex]25=25a[/tex]
Divide both sides by 25.
[tex]a=1[/tex]
The required function is
[tex]f(x)=(1)(5)^x[/tex]
Therefore the exponential function is [tex]f(x)=5^x[/tex]. Option 4 is correct.
