(Euclid 2024, Question 3, CEMC - UWaterloo)

(a) The graph of the equation $y=r(x-3)(x-r)$ intersects the $y$-axis at $(0, 48)$. What are the two possible values of $r$?
(b) A bicycle costs $\$B$ before taxes. If the sales tax were $13\%$, Annemiek would pay a total that is $\$24$ higher than if the sales tax were $5\%$. What is the value of $B$?
(c) The function $f$ has the following three properties:

• $f(1)=3$.
• $f(2n)=(f(n))^2$ for all positive integers $n$.
• $f(2m+1)=3f(2m)$ for all positive integers $m$.

Determine the value of $f(2)+f(3)+f(4)$.

Answer Submission Note(s)
In part (a), sort your answers in ascending order and separate them with a comma.
Separate the answers for each part with a single space.
For example: "a1,a2 b c"