Answer:
The Answer is D.
Step-by-step explanation:
To solve this question we should use the process of elimination.
We can clearly see that the function f(x) increases as x increases so we can rule out options A and C.
Now we have to decide between B and D.
So the format for a quadratic function is [tex]f(x)=ax^2+bx+c[/tex]
The format for an exponential function is [tex]f(x)=a*b^x[/tex]
So let's try exponential first:
at x = 0 we solve for a and b:
[tex]10000 = a*b^0\\10000=a[/tex]
so we find b when x =5
[tex]12201.9 =10000b^5\\b^5=\frac{12201.9}{10000} \\b^5=1.22019\\b=\sqrt[5]{1.22019} \\[/tex]
b = 1.04060
Then we evaluate the value as x=10
[tex]14888.64=10000b^10\\b^10=14888.64/10000\\b^10=1.488864\\b=\sqrt[10]{1.488864} \\b=1.04060[/tex]
As can be seen from both cases b is the same. This is a key chareteristic of an exponential function. So the Answer is D.
