Write the equation for an exponential function, in the form y=a•b^x, whose graph passes through the coordinate points (1,7.5) an

d (3,16.875)

Mathematics

1 answer:

Olegator [25]3 years ago

5 0

$\bf (\stackrel{x}{1}~~,~~\stackrel{y}{7.5})\implies 7.5=ab^1\implies \boxed{7.5=ab} \\\\\\ (\stackrel{x}{3}~~,~~\stackrel{y}{16.875})\implies 16.875=ab^3\implies 16.875=ab^{1+2}\implies 16.875=abb^2 \\\\\\ 16.875=\boxed{7.5}b^2\implies \cfrac{16.875}{7.5}=b^2\implies 2.25=b^2 \\\\\\ \sqrt{2.25}=b\implies \blacktriangleright 1.5=b \blacktriangleleft \\\\[-0.35em] ~\dotfill$

$\bf 7.5=ab\implies \cfrac{7.5}{b}=a\implies \cfrac{7.5}{1.5}=a\implies \blacktriangleright 5=a \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=5(1.5)^x~\hfill$

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