Answer:
Here is the complete question (attachment).
The function which represent the given points are [tex]f(x)=8(2)^{x}[/tex]
Step-by-step explanation:
We know that a general exponential function is like,[tex]y=a(b)^{x}[/tex]
We can find the answer by hit and trial method by plugging the values of [tex](x,y)[/tex] coordinates.
Here we are going to solve this with the above general formula.
So as the points are [tex](1,16)[/tex] then for [tex]x=1,\ y=16[/tex]
Can be arranged in terms of the general equation.
[tex]ab^1=16[/tex]...equation(1) and [tex]ab^4=128[/tex]...equation(2)
[tex]a\times b=16, then\ a=\frac{16}{a}[/tex]
Plugging the values in equation 2.
We have
[tex]\frac{16}{b} b^4=128,16\times b^3=128,b=\sqrt[3]{\frac{128}{16}} =\sqrt[3]{8}=2[/tex]
Plugging [tex]b=2[/tex] in equation 1.
We have [tex]a=\frac{16}{b} =\frac{16}{2} =8[/tex]
Comparing with the general equation of exponential [tex]a=8[/tex] and [tex]b=2[/tex]
So the function which depicts the above points =[tex]y=8(2)^x[/tex]
From theoption we have B as the correct answer.
