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ser-zykov [4K]
4 years ago
15

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]4 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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Explanation:
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Now that we know a=100 we can find the exterior angle. a+x=180 because the angles are on a straight line which equals 180°

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