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2-72.

Find the equation of an exponential function that passes through each pair of points. 2-72a HW eTool (Desmos) and 2-72b HW eTool (Desmos). Homework Help ✎.

1. (2, 9) and (4, 324)

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Use the equation $y=ab^x$ to help you here. Begin by substituting one of the points for x and y.

Next, substitute the other ordered pair for x and y.

$9=ab^{2}$

$a=\frac{9}{b^{2}}$

Use substitution, and solve for b.

$324=ab^{4}$

$a=\frac{324}{b^{4}}$

Now, solve for a.

$\frac{9}{b^{2}}=\frac{324}{b^{4}}$

$9b^{4}=324b^{2}$

$9b^{2}=324$

$b^{2}=36$

$b=6$

$y = 0.25\cdot 6^{x}$

2. (−1, 40) and (0, 12)

$y=12\cdot0.3^x$