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 ):
Question
Answer:
ANSWERB)
[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.
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