Question

The total number of people infected with a virus often grows like a logistic curve. Suppose that 10 people originally have the virus, and that in the early stages of the virus (with time, t , measured in weeks), the number of people infected is increasing exponentially with K=1.6 . It is estimated that, in the long run, approximately 6750 people become infected.

Use this information to find a logistic function to model this situation.

P=?
The total number of people infected with a virus often grows like a logistic curve. Suppose that 10 people originally have the virus, and that in the early stages of the virus (with time, t , measured in weeks), the number of people infected is increasing exponentially with K=1.6 . It is estimated that, in the long run, approximately 6750 people become infected.

Use this information to find a logistic function to model this situation.

P=?
@Mathematics

Answer 1

6750 because if it has a long time to spread it eventually gets everyone

Answer 2

so do i do

10=1650/1+be^(k(0)) then solve for b?

Answer 3

you have to use the P=L/(1+be^(-kt))

Answer 4

somehow

Answer 5

it doesn't specify the time in weeks when this occurs

Answer 6

\[\frac{dP}{dt}=1.6P\left(1 - \frac{P}{6750}\right)\]

Answer 7

right it is a differential equation

Answer 8

Valpey can you continue?

Answer 9

sure we have to separate the variables all the p's on one side and the dt term on the right. We then integrate both sides.

Answer 10

separable first order

Answer 11

i got (6750)/1+674e^-(1.6t)

Answer 12

i got it right