How do you find the equation of the exponential function $y=a(b)^x$ which goes through the points(2, 18) and (6,91.125). What is the intercepts of this function?

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Answer 1 · 2017-02-20T05:52:53

$y=8(5/4)^x$
intercept: $(0;8)$

It's
$a*b^2=18$ and $a* b^6=91.125$ and $b>0$

then

$a=18/b^2$ and $18/b^2*b^6=91.125$

$a=18/b^2$ and $18*b^4=91.125$

$a=18/b^2$ and $b^4=91.125/18=5.0625$

$a=18/b^2$ and $b^2=2.25$

$a=18/2.25$ and $b=1.25$

$a=8$ and $b=5/4$

Then $y=8(5/4)^x$

If $x=0$ , then $y=8*(5/4)^0=8*1=8$

It's the one intercept of the function since $y=0 AAx$
graph{8*(5/4)^x [-10, 5, -1, 15]}

How do you find the equation of the exponential function y=a(b)^xy=a(b)^x which goes through the points(2, 18) and (6,91.125). What is the intercepts of this function?