Question

Contagious diseases can spread very quickly. Suppose five people are ill during the first week of an epidemic and that each person who is ill spreads the disease to four people by the end of the next week. By the end of the tenth week of the epidemic, how many people have been affected by the illness?

Answer 1

@mathmate

Answer 2

If we start with 1 sick person, then
week #of sick people
0 1
1 5
2 25
3 125
...
n 5^n

So this is an exponential function.
Can you figure out the rest?

Answer 3

no

Answer 4

The rule would be
f(n)=a(5^n)

where
f(n)=number of sick people at the end of n weeks.
a=number of sick people at the start
n=number of weeks