Rachel M.

asked • 03/16/16

PreCalculus Algebra Exponential Functions

I feel like I almost got this but I need help please!! Question is: Let f(x)=2^x. Show that (f(x+h)-f(x))/h = 2^x((2^h-1)/h)

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Arnold F. answered • 03/16/16

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Just factor 2x in the numerator: remember 2x+h = 2x2h.
 
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Rachel M.

thank you, i remember that, maybe i'm over thinking it. I have so far: (2^x2^h-1(2^x))/h = 2^x((2^h-1)/h)
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03/16/16

Arnold F.

What you have is exactly what you want to show.
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03/16/16

Rachel M.

there isn't another step to show that they are the same?
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03/16/16

Arnold F.

I'm not sure where you are stuck.
 
[f(x+h) - f(x)]/h = [2x+h - 2x]/h = [2x2h - 2x]/h = [2x(2h - 1)] /h
 
 
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03/16/16

Rachel M.

the way you just wrote it made me understand, i was trying to figure out how to get rid of one of those 2^x but i see you factor it out to make it look like the other equation. Thank you!
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03/16/16

Arnold F.

You're welcome Rachel. Glad I could help.
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03/16/16

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