SOLUTION: Find an equation of the form f(x) = a*b^x/t to fit the values below: <pre> x = 0 10 20 30 40 f(x)= -4 -16 -64 -256 -1024 </pre> I tried using the TI-84 Plus to dev

Algebra ->  Exponents -> SOLUTION: Find an equation of the form f(x) = a*b^x/t to fit the values below: <pre> x = 0 10 20 30 40 f(x)= -4 -16 -64 -256 -1024 </pre> I tried using the TI-84 Plus to dev      Log On


   

Question 800647: Find an equation of the form f(x) = a*b^x/t to fit the values below:
x =    0   10	 20	  30	   40
f(x)= -4  -16	-64	-256	-1024

I tried using the TI-84 Plus to develop a equation out of this using Stat Plot but it keeps coming back with a error message.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Our challenge is to find values for and such that 
x =    0   10	 20	  30	   40
f(x)= -4  -16	-64	-256	-1024

First we know that , so , but since , it follows that

Then, now that we know the value for , we can write:



which is to say:



taking the natural log of both sides:



then



But , so







John

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