Chantalkitakaidn
Answered

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Assume there is a virus in a town, and there exists one patient on day 1.

Assume that the patient transmits the virus to another person once per day, then this other person becomes a patient, and that all carriers spread the virus at the same rate, i.e. each patient passes the virus on to one other person per day.

Once someone has caught the virus, they do not catch it again.

The town has a fixed population of 700000

and the borders are closed so that no one can enter or exit the town.

How many days does it take to make everyone in the town catch the virus?

Sagot :

Using an exponential function, it is found that it takes 20 days for everyone in the town to catch the virus.

What is an exponential function?

An exponential function is given as follows:

[tex]y = ab^x[/tex]

In which:

  • a is the initial value.
  • b is the rate of change.

For this problem, we have that:

  • On the first day, one person has the virus.
  • On the second day, the first person transmitted the virus to another person, hence two people have the virus.
  • On the third day, each of the two people transmitted the virus to another two, hence four people have the virus.

From this, we get that the parameters are given as follows:

a = 1, b = 2.

Hence the function for the number of contaminated people after t days is given by:

[tex]f(t) = 2^t[/tex]

Now, we have to solve for t when f(t) = 700000, hence:

[tex]2^t = 700000[/tex]

[tex]\log{2^t} = \log{700000}[/tex]

[tex]t\log{2} = \log{700000}[/tex]

t = log(700000)/log(2)

t = 19.4, rounded to 20.

It takes 20 days for everyone in the town to catch the virus.

More can be learned about exponential functions at https://brainly.com/question/25537936

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