Question

Find the formula for an exponential function that passes through the two points given.

(x, y) = (0, 4)
and
(x,y) = (3, 108)

Answer 1

`\bf y = ab^x \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{0}~~,~~\stackrel{y}{4})\qquad \qquad 4=ab^0\implies 4=a(1)\implies 4=a~\hfill \boxed{y = 4b^x} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{3}~~,~~\stackrel{y}{108})\qquad \qquad 108=4b^3\implies \cfrac{108}{4}=b^3\implies 27=b^3 \\\\\\ 3^3=b^3\implies 3=b \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=4(3)^x~\hfill`