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?

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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?

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Answer 1 · 2018-06-07T10:56:45

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 $n=log_2(2000)$ .

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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?

1 Answer

Explanation:

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