Question

2. Let’s pretend that in an American city there were 2000 new cases on Monday which is a 12% decrease from two weeks ago. So it appears that new covid cases are going down (wahoo!) with a two-week trend of -12%. How many new cases were there two weeks ago? (don’t round for accuracy)

Answer 1

22

Explanation:

Let the number of new cases two weeks ago = x

After a decrease of 12%, the number of new cases on Monday = 2000.

So, we have that:

`\begin{gathered} x-12\%\text{ of x}=2000 \\ x-0.12x=2000 \end{gathered}`

The equation is then solved for x:

`\begin{gathered} 0.88x=2000 \\ \text{ Divide both sides by 0.88} \\ (0.88x)/(0.88)=(2000)/(0.88) \\ x=2000/(88)/(100) \\ x=2000*(100)/(88) \\ =2000*(25)/(22) \\ x=2272(8)/(11) \end{gathered}`

There were approximately 2,273 new cases two weeks ago.