Question

The diagram shows the graph of y=x^n , where n is an integer. Given that the curve passes between the point (2 , 200) and (2, 2000) , determine the value of n?

Answer 1

The question is somehow strange, I tried to interpret it.
Let me know if you meant anything else.

Explanation:

We have `y=x^n`, and some `(x,y)` couples to plug in the question to solve for `n`.

The first couple is `(2,200)`, which means that

`200 = 2^n`

The second couple is `(2,2000)`, which means that

`2000 = 2^n`

Now, these two conditions can't be true at the same time, since `2^n` should equal both `200` and `2000`, which are clearly different.

So, the best you could do is solve separately: if `y=x^n` passes through `(2,200)`, then you have `200=2^n` and thus, taking logarithm base `2` to both sides, you have

`n = log_2(200)`

Similarly, in the other case, you have `n=log_2(2000)`.