Respuesta :
Answer:
25.2 weeks until everyone on the planet is infected
Step-by-step explanation:
The number of infected people after t weeks has the following format:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the initial number of infected people and r is the growth rate, as a decimal.
The number of infected people doubles every week
This means that [tex]P(1) = 2P(0)[/tex]
So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]2P(0) = P(0)(1+r)[/tex]
[tex]1 + r = 2[/tex]
[tex]r = 1[/tex]
So
[tex]P(t) = P(0)*(2)^{t}[/tex]
200-person town
This means that [tex]P(0) = 200[/tex]
So
[tex]P(t) = P(0)*(2)^{t}[/tex]
[tex]P(t) = 200*(2)^{t}[/tex]
How long will it be until everyone on the planet is infected?
This is t for which P(t) = 7700000000[/tex]
So
[tex]P(t) = 200*(2)^{t}[/tex]
[tex]7700000000 = 200*(2)^{t}[/tex]
[tex]2^{t} = \frac{7700000000}{200}[/tex]
[tex]\log{2^{t}} = \log{\frac{7700000000}{200}}[/tex]
[tex]t\log{2} = \log{\frac{7700000000}{200}}[/tex]
[tex]t = \frac{\log{\frac{7700000000}{200}}}{\log{2}}[/tex]
[tex]t = 25.2[/tex]
25.2 weeks until everyone on the planet is infected
