Question

1. Pretend that in a certain city the number of new cases of COVID wasreported to be 200 new cases on Sunday. Let's pretend that thenumber of new cases grows by 22% on Monday, and then after thatfalls by 22% on TuesdayQuestion C. What percent would the percent increase have to be on Mondayto have a total change of zero% from Sunday to Tuesday? i.e.new covid cases go up by ???% on Monday and then down 22%on Tuesday for a total change of zero%. (Be accurate with ananswer like 1.23%)

Answer 1

EXPLANATION :

a. Since we are talking about the number of cases, our answer must be a whole number.

On Sunday, there are 200 new cases, it grows by 22% on monday.

22% of 200 is 0.22 x 200 = 44

So on Monday, there are 200 + 44 = 244 new cases

Then it falls by 22%.

22% of 244 is 0.22 x 244 = 53.68

So on Tuesday, there are 244 - 53.68 = 190.32 new cases

To summarized :

Monday : 244 new cases

Tuesday : 190.32 new cases

b. Growing 22% and falling 22% will not make a 0% in total by the result we have above.

From 200 on Sunday, it became 190.32 on Tuesday.

The percent change from Sunday to Tuesday is :

`\begin{gathered} \%=\frac{\text{ Tuesday - Sunday}}{\text{ Sunday}}*100=(190.32-200)/(200)*100 \\ \\ \%=-4.84\% \end{gathered}`

-4.84%, negative since the number of new cases on Tuesday is less than the number of new cases on Sunday.

c. For the total change to be 0% from Sunday to Tuesday, the number of new cases on Tuesday must be equal to the number of new cases on Sunday and that's 200.

Let N = number of new cases on Monday, falls by 22% on Tuesday and the result must be 200.

Following the same steps we have from letter a :

22% fall on Tueday :

22% of N is 0.22N

The number of new cases on Tuesday will be :

N - 0.22N = 200

Solve for N :

`\begin{gathered} N-0.22N=200\text{ } \\ 0.78N=200 \\ \\ N=(200)/(0.78) \\ \\ N=256.41 \end{gathered}`

So the number of cases on Monday must be 256.41

Now, we need to find the growth rate from Sunday of 200 new cases to Monday of 256.41 new cases.

Let x = percent growth

Then :

`\begin{gathered} 200+x(200)=256.41 \\ 200x=256.41-200 \\ 200x=56.41 \\ \\ x=(56.41)/(200)=0.28205 \\ \\ \text{ Multiply by 100 :} \\ 0.28205*100=28.205\% \end{gathered}`

Therefore, the percent increase on Monday should be 28.205%