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

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