Question

The spread of a flu virus on a college campus is modeled by y= 5000/(1+4999e^-0.8t), where y is the number of students infected after t days.
1) How many students are infected after 8 days?
2) How many days will it take before half of the student population is infected?

Answer 1

Answer:

i got the same for the first and the second works out so i think he is right^

Step-by-step explanation:

Answer 2

Answer:

537 students

11 days

Step-by-step explanation:

       5000

y=  -----------------

    (1+4999e^-0.8t)

a)  after 8 days  means t =8

       5000

y=  -----------------

    (1+4999e^-0.8*8)

       5000

y=  -----------------

    (1+4999e^-6.4)

       5000

y=  -----------------

    (1+8.306)

       5000

y=  -----------------

    (9.306)

y =537.28

Rounding to the nearest student

y = 537 students

b)  1/2 the student population  means y =2500  (The 5000 is the student population)

             5000

2500=  -----------------

        (1+4999e^-0.8t)

Multiply each side by  (1+4999e^-0.8t)

2500 (1+4999e^-0.8t) = 5000

Divide each side by 2500

(1+4999e^-0.8t) = 5000/2500

(1+4999e^-0.8t) = 2

Subtract 1

(4999e^-0.8t) = 2-1

(4999e^-0.8t)=1

Divide by 4999

(4999/4999e^-0.8t)=1/4999

e^-0.8t=1/4999

Take the natural log of each side

ln(e^-0.8t)=ln(1/4999)

-.8t = ln(1/4999)

Divide by -.8

-.8/-8t = -1/.8 *ln(1/4999)

t = -1/.8 *ln(1/4999)

t≈10.6462

Rounding, it will take 11 days