How do you find the equation of an exponential function that passes through the points (1,2) and (3,32)?

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Answer 1 · 2018-05-13T01:15:39

$y = \frac{4^{x}}{2}$ $y=4^x/2$

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A general form of an exponential function would be:

$y = a b^{x}$ $y=ab^x$

Let's plug in the coordinates:

$2=ab^1, :. ab=2, :. a=2/b=2b^(-1)$

$32=a(b)^3$

$32=2b^(-1)b^3$

$32=2b^2$

$16=b^2$

$b=4, :. a=2/b=2/4=1/2$

$y=(1/2)4^x$

$y=4^x/2$