Question

There are three parts to this question. A) The number of people initially infected is? (round to the nearest whole number as needed)

Answer 1

a.

To find the initial number of people infected, let's calculate the value of f(t) for t = 0:

`f(0)=(102000)/(1+5200e^0)=(102000)/(1+5200)=(102000)/(5201)=19.61`

Rounding to the nearest whole number, the initial value is 20 people.

b.

Using t = 4, let's calculate the value of f(t):

`f(4)=(102000)/(1+5200e^(-4))=(102000)/(1+5200\cdot0.0183156)=(102000)/(96.24112)=1.059.84`

Therefore the number of infected people is 1060.

c.

When t tends to infinity, the value of 5200e^-t will tend to zero, therefore we have:

`\lim_(t\to\infty)f(t)=(102000)/(1+0)=102000`

Therefore the limiting size is 102000 people.