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:
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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