adarascarlet80
2022-10-08
Answered

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

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domino671v

Answered 2022-10-09
Author has **8** answers

Let the exponential function be

$$y=a{b}^{x}$$

At $$(-2,1),\text{}a{b}^{-2}=1$$

At $$(3,32),\text{}a{b}^{3}=32$$

Now,

$$\frac{a{b}^{3}}{a{b}^{-2}}=\frac{32}{1}\phantom{\rule{0ex}{0ex}}\Rightarrow {b}^{5}=32={2}^{5}\phantom{\rule{0ex}{0ex}}\Rightarrow b=2\phantom{\rule{0ex}{0ex}}\therefore a=\frac{32}{{b}^{3}}=\frac{32}{8}=4$$

Hence the exponential function is

$$y={4.2}^{x}$$

$$y=a{b}^{x}$$

At $$(-2,1),\text{}a{b}^{-2}=1$$

At $$(3,32),\text{}a{b}^{3}=32$$

Now,

$$\frac{a{b}^{3}}{a{b}^{-2}}=\frac{32}{1}\phantom{\rule{0ex}{0ex}}\Rightarrow {b}^{5}=32={2}^{5}\phantom{\rule{0ex}{0ex}}\Rightarrow b=2\phantom{\rule{0ex}{0ex}}\therefore a=\frac{32}{{b}^{3}}=\frac{32}{8}=4$$

Hence the exponential function is

$$y={4.2}^{x}$$

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