write an exponential function whose graph passes through points (5,729) and (3,81)

Question

anonymous · Answer

@Luigi0210

luigi0210 · Answer

Well it has a base of 3

anonymous · Answer

ok how did you get that equation

luigi0210 · Answer

Lucky guessing

anonymous · Answer

lol

anonymous · Answer

you can actually compute it without guessing if you like

anonymous · Answer

you are told $(3,81)$ is on the graph of $y=ab^x$ which means $81=ab^3$ 
similarly you know $729=ab^5$ divide the second by the first

anonymous · Answer

this tells you 
$$\frac{729}{81}=\frac{ab^5}{ab^3}$$ or 
$$9=b^2$$ making $b=3$
guessing is good too!

anonymous · Answer

really how... because if I can get the idea of how to do one I may be able to DO the other problems I have by myself.

anonymous · Answer

then since $81=a\times 3^3=27a$ you know $a=3$ as well

luigi0210 · Answer

haha, satellite's a genius

anonymous · Answer

making the function 
$$f(x)=3\times 3^x$$ or more commonly written as $$f(x)=3^{x+1}$$

luigi0210 · Answer

my equation again: 
$$y=3^{x+1}$$

anonymous · Answer

like i said, guessing is a good method as well

luigi0210 · Answer

And sorry ML, once you get enough practice these will be second nature to you

anonymous · Answer

OK thank YOU guys I will go on & try to do the others with this blueprint