Question 248007
{{{f(x) = Ca^x}}} Start with the given equation.



{{{18 = Ca^1}}} Plug in {{{f(x)=18}}} and {{{x=1}}}



{{{18 = Ca}}} Simplify



{{{18/a = C}}} Divide both sides by 18.



So {{{C=18/a}}}



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{{{f(x) = Ca^x}}} Go back to the given equation.



{{{9 = Ca^2}}} Plug in {{{f(x)=9}}} and {{{x=2}}}



{{{9 = (18/a)a^2}}} Plug in {{{C=18/a}}}



{{{9 = (18a^2)/a}}} Multiply



{{{9 = 18a}}} Reduce



{{{9/18 = a}}} Divide both sides by 18.



{{{1/2=a}}} Reduce.



So {{{a=1/2}}}. So the value of C is {{{C=18/a=18/(1/2)=18(2/1)=36}}} giving us the function {{{f(x)=36(1/2)^x}}}