Question

Assuming that when a virus breaks out, an infected person can infect multiple unaffected people. In a particularly type of flu outbreak at an elementary school, the number of infected people triples each day in the first school week of January. If 5 people were sick with the flu on Monday, find the equation which best predicts the number of infected people, I(d), d days after Monday?

• A. $I\left(d\right)=5\times {3d}^2$
• B. $I\left(d\right)=5d^3$
• C. $I\left(d\right)=5\times 3^d$
• D. $I\left(d\right)=5\times 9d$

Answer 1

The correct option is C $I\left(d\right)=5\times 3^d$

Whenever there are variables in the question and in the answer choices, think Plugging In. Let d = $2$. On the first day after Monday, $5\times 3=15$ people will be infected. On the second day after Monday, $15\times 3=45$ people will be infected.
Therefore, when d = $2$, the result is $45$. Plug $2$ in for d in the answer choices to see which answer equals the target number of $45$. Choice (A) becomes $5\times 3(2{)}^2$ = $5\times 12=60$. This does not match the target number, so eliminate (A). Choice (B) becomes $5\times 2^3=40$. Eliminate (B). Choice (C) becomes $5\times 3^2=45$. Keep (C), but check the remaining choice just in case. Choice (D) becomes $5\times 9\left(5\right)=225$.
So Eliminate (D), and choose (C).