Question

Which describes the function over the interval given in the table?

Answer 1

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 $f(x)=ax^2+bx+c$

The format for an exponential function is $f(x)=a*b^x$

So let's try exponential first:

at x = 0 we solve for a and b:

$10000 = a*b^0\\10000=a$

so we find b when x =5

$12201.9 =10000b^5\\b^5=\frac{12201.9}{10000} \\b^5=1.22019\\b=\sqrt[5]{1.22019}$

b = 1.04060

Then we evaluate the value as x=10

$14888.64=10000b^10\\b^10=14888.64/10000\\b^10=1.488864\\b=\sqrt[10]{1.488864} \\b=1.04060$

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.