SOLUTION: y=1000(2raised to the -.1x) if x=10, what is y=? then, if y=250, what is x=?

Question 367073: y=1000(2raised to the -.1x)
if x=10, what is y=?
then, if y=250, what is x=?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

It help to rewrite this with a positive exponent. In general, . so your expression can be rewritten as:

if x = 10...

which simplifies as follows:

if y = 250...

Divide both sides by 1000:

which simplifies to:

This is a proportion so we can cross multiply:

The shortest way to solving for x here is to recognize that both sides of the equation are powers of two:

(Note: If both sides had not both been powers of the same number, then we would have to use logarithms to solve for x.)
The only way for powers of 2 to be equal is if their exponents are equal. So:

And finally we can multiply both sides by 10:

which simplifies to:

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