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If \( f(x) \) is an exponential function where \( f(-1.5) = 27 \) and \( f(7) = 83 \), find the value of \( f(-0.5) \) to the nearest hundredth.

Answer :

Answer:

[tex]f(x) = a {b}^{x} [/tex]

[tex]f( - 1.5) = a {b}^{ - 1.5} = 27[/tex]

[tex]f(7) = a {b}^{7} = 83[/tex]

[tex] {b}^{8.5} = \frac{83}{27} [/tex]

[tex]b = \sqrt[8.5]{ \frac{83}{27} } = 1.14124[/tex]

[tex]a( {1.14124}^{7} ) = 83[/tex]

[tex]a = 32.91781[/tex]

[tex]f(x) = 32.91781( {1.14124}^{x} )[/tex]

[tex]f( - 0.5) = 30.81[/tex]

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