# Find a formula for the exponential function passing through the points (-2, 1) and (3, 32).

Find a formula for the exponential function passing through the points (-2, 1) and (3, 32).
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domino671v
Let the exponential function be
$y=a{b}^{x}$
At
At
Now,
$\frac{a{b}^{3}}{a{b}^{-2}}=\frac{32}{1}\phantom{\rule{0ex}{0ex}}⇒{b}^{5}=32={2}^{5}\phantom{\rule{0ex}{0ex}}⇒b=2\phantom{\rule{0ex}{0ex}}\therefore a=\frac{32}{{b}^{3}}=\frac{32}{8}=4$
Hence the exponential function is
$y={4.2}^{x}$