## Euclid 2024 Question 3, CEMC UWaterloo

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#### Difficulty: 6

#### This problem is tagged with euclid, euclid24, highschool.

**(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 $m$.

*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"

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