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# Exponential functions

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If f(x) is an exponential function where f(3) = 18 and f(7.5) = 60, then find thevalue of f(12), to the nearest hundredth.

Apr 3, 2021

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Let us say that, because $f(x)$ is an exponential function, you write it as $f(x)=a*b^x$. To get from $a*b^3$ to $a*b^{7.5}$, you multiply by $\frac{10}{3}$. So that means to go up another 4.5 x, to 12, you multiply by another $\frac{10}{3}$. So $f(12)=60*\frac{10}{3}=20*10=\boxed{200}$.

I am not one hundred percent sure about this solution because it says round to the nearest hundredth and my number is a whole integer, but try it anyways. I hope it works :)

Apr 3, 2021