Initially, 10 people have an infection. The next day, every infected person infects one more person. If this pattern continues, how many days will it take for 1280 people to be infected?
a) 7 days
b) 64 days
c) 10 days
d) 128 days
10 * 2^d = 128
I think R_scott meant to say
10* 2^d = 1280
then
2^d = 128
we know 2^7 = 128
so d = 7
To solve this problem, we need to determine the number of days it takes for the infection to spread from 10 people to 1280 people.
Let's analyze the pattern of infection. Initially, there are 10 infected people. On the next day, each of these infected individuals will infect one more person. This means that the number of infected people doubles each day.
So, on the first day, there are 10 infected people.
On the second day, there are 10 infected people + 10 newly infected people = 20 infected people.
On the third day, there are 20 infected people + 20 newly infected people = 40 infected people.
On the fourth day, there are 40 infected people + 40 newly infected people = 80 infected people.
And so on.
We can see that the number of infected people doubles each day. Therefore, we can represent the number of infected people as a power of 2, where n is the number of days it takes for the infection to spread.
2^n = 1280
To solve this equation, we can take the logarithm of both sides with base 2:
n = log2(1280)
Using a calculator, we can find that log2(1280) is approximately 10. Therefore, it will take approximately 10 days for 1280 people to be infected.
So, the correct answer is option c) 10 days.