Which function equation is represented by the graph? A)f(x)=40(3.25)^xB) f(x)=40(2.25)^xC) f(x)=40(1.5)^xD) f(x)=40(2.5)^xPLEASEE HELP ):

ANSWER

B)
[tex]f(x) = 40( {2.25})^{x} [/tex]



EXPLANATION

Let the function be of the form

[tex]f(x) = a( {b})^{x} [/tex]

Then the point (0,40) lies on the graph of this function. This point must satisfy the equation of the function.

We substitute the point to get,


[tex]40 = a( {b})^{0} [/tex]


This implies that,


[tex]40 = a( 1)[/tex]


[tex]40 = a[/tex]

We substitute a=40 into the function equation to get,


[tex]f(x) = 40( {b})^{x} [/tex]
The point (1,90) also lies on the graph of the function. This gives us,


[tex]90= 40( {b})^{1} [/tex]


[tex]90= 40b[/tex]



[tex] \frac{90}{40} = b[/tex]

[tex]b = 2.25[/tex]



We substitute the value of b also into function to get,



[tex]f(x) = 40( {2.25})^{x} [/tex]

The correct answer is B.