To determine: C and a so that f(x)=Ca^{x} satisfies given conditions.

To determine: C and a so that $$\displaystyle{f{{\left({x}\right)}}}={C}{a}^{{{x}}}$$ satisfies given conditions.
Given: $$\displaystyle{f{{\left({0}\right)}}}={3};{f{{\left({3}\right)}}}={24}$$

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StrycharzT
Formula used:
If $$\displaystyle{b}^{{{x}}}={a}^{{{x}}}$$ with $$\displaystyle{a},{b}{>}{0}$$ then $$\displaystyle{b}={a}$$.
Calculation:
Consider the given function $$\displaystyle{f{{\left({x}\right)}}}={C}{a}^{{{x}}}$$. Substituting $$\displaystyle{x}={0}$$ we get
This gives, $$\displaystyle{C}={3}$$.
Substituting $$\displaystyle{x}={3}\in{f{{\left({x}\right)}}}={3}{a}^{{{x}}}$$ we get
$$\displaystyle{f{{\left({3}\right)}}}={24}={3}{a}^{{{3}}}$$
$$\displaystyle{a}^{{{3}}}={\frac{{{24}}}{{{3}}}}$$
$$\displaystyle{a}^{{{3}}}={8}={2}^{{{3}}}$$
This gives $$\displaystyle{a}={3}$$.
Conclusion:
From the given conditions we find $$\displaystyle{f{{\left({x}\right)}}}={3}{\left({2}^{{{x}}}\right)}$$