Question

day of a measles outbreak at a school, 8 students were identified to have the measles. Each day for the On the first following two weeks, the number of new cases doubled from those identified with the disease the day prior How many students are identified to have measles in all at the end of the 6th day of the outbreak

A. 386
B.415
C.483
D.504

Answer 1

Answer:

D. 504

Step-by-step explanation:

Let the number of days = x

Now, the number of students doubles each day for the two weeks with the initial number of students having measles = 8.

So, we have,

Days (x)                  Cases doubled                      Number of Students

1                                       8                                                8

2                                      8 × 2                                         16

3                                      16 × 2                                        32

4                                      32 × 2                                       64

So, we get the geometric series as 8, 16, 32, 64,...... for two weeks.

Then, the common ratio = $\frac{16}{8}=\frac{32}{16}$ = 2

Thus, Number of students = $8\times \frac{(1-2^6)}{1-2}$

i.e. Number of students = $8\times \frac{(1-64)}{-1}$

i.e. Number of students = $8\times \frac{(-63)}{-1}$

i.e. Number of students = 8 × 63 = 504

Hence, the number of students having measles at the end of the 6th day are 504.

Answer 2

Answer: 504

I know that this is correct because I just took a test with this question and I got 100%.