Question

The functions f(x) and g(x) are shown below:

f(x) = 0.05x
g(x) = (0.05)x

Which statement best describes the graph of f(x) and g(x)?

The graph of g(x) will eventually exceed the graph of f(x).

The graph of f(x) will eventually exceed the graph of g(x).

The graphs will both have their y-intercept equal to 1.

The graphs will both have their y-intercept equal to 0.05

Answer 1

@mathstudent55

Answer 2

Are there exponents here?

Answer 3

OH yes the g(x)=(0.05) ^x

Answer 4

0.05x is the same as (0.05)x

Do you mean \(f(x) = 0.05x\) and \(g(x) = (0.05)^x\) ?

Answer 5

yes

Answer 6

Ok, I see it.

Answer 7

i think B is the correct answer

Answer 8

For g(x), you have a base of 0.05 and an exponent of x.
As x gets larger, g(x) will get smaller.

Answer 9

When you have a number between 0 and 1, the larger the exponent, the smaller the result.

For example:
\((\dfrac{1}{10})^1 = \dfrac{1}{10} \)

\((\dfrac{1}{10})^2 = \dfrac{1}{100} \)

\((\dfrac{1}{10})^3 = \dfrac{1}{1000} \)

\((\dfrac{1}{10})^4 = \dfrac{1}{10000} \)

Notice the base is 1/10, a number between 0 and 1.
As the exponent goes from 1 to 2 to 3, etc. the result is getting smaller and smaller.

Answer 10

so is it b

Answer 11

In your case, the base is 0.05, which is the same as 1/20, but the result is the same, as the exponent increases, g(x) decreases.

Answer 12

Yes.
Now think of f(x).
It is simply 0.05 * x
Even though you are always multiplying x by 0.05, as x gets larger and larger, 0.05 * x also increases.

Answer 13

This may help you visualize this:

http://www.wolframalpha.com/input/?i=plot%3A+f%28x%29+%3D+0.05x%3B+g%28x%29+%3D+0.05^x