ilovewolfs22
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PLEASE HELP WILL GIVE BRAINLIEST 

The function y=10,942(1.175)^n represents the population of nates hometown, where n is the # of decades since 1960. Nate wants to rewrite the function to show growth per year. He rewrites the function as y=10,942(1.175)^n Where n is now the # of years since 1960. Did he write it correctly? If so explain why, if not explain why and write the correct function

Respuesta :

mathmate
Nate did not write correctly.  His function is identical to the century function.

The new function needs to be
[tex]y=10942(1.175^{1/10})^n[/tex] where n is now every year since 1960.

Check: if n=10, then y= population 10 years from 1960, or 1970
[tex]y=10942(1.175^{1/10})^{10}[/tex]
=>
[tex]y=10942(1.175^{1/10 * 10 })[/tex]
[tex]y=10942(1.175^{1})[/tex]   as in the original equation for 1 decade from 1960

Note: [tex]1.175^{1/10}=1.016257553692097[/tex]  approximately

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