High School

If \( f(x) \) is an exponential function where \( f(3.5) = 21 \) and \( f(6.5) = 69 \), then find the value of \( f(9) \), to the nearest hundredth.

Answer :

Where the above is given, note that the value of f(9) to the nearest hundredth is 10.80.

To solve,

Make y = aˣ

That is:

[tex]a^{6.5}[/tex] = 6.9

[tex]a^{3.5}[/tex] = 21

[tex]a^{6.5}/ a^{3.5}[/tex] = 69/21

= a³

Since a⁹ = (a³)²
= (69/21)²

= 10.7959183673

≈ 10.80

Thus, the value of f(9) to the nearest hundredth is approximately 10.80

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