Question

There are approximately 7.7 billion humans on Earth. If the virus spreads beyond the 200-person town, how long will it be until everyone on the planet is infected if the number of infected people doubles every week?

Answer 1

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:

$P(t) = P(0)(1+r)^{t}$

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 $P(1) = 2P(0)$

So

$P(t) = P(0)(1+r)^{t}$

$2P(0) = P(0)(1+r)$

$1 + r = 2$

$r = 1$

So

$P(t) = P(0)*(2)^{t}$

200-person town

This means that $P(0) = 200$

So

$P(t) = P(0)*(2)^{t}$

$P(t) = 200*(2)^{t}$

How long will it be until everyone on the planet is infected?

This is t for which P(t) = 7700000000[/tex]

So

$P(t) = 200*(2)^{t}$

$7700000000 = 200*(2)^{t}$

$2^{t} = \frac{7700000000}{200}$

$\log{2^{t}} = \log{\frac{7700000000}{200}}$

$t\log{2} = \log{\frac{7700000000}{200}}$

$t = \frac{\log{\frac{7700000000}{200}}}{\log{2}}$

$t = 25.2$

25.2 weeks until everyone on the planet is infected