An infection is spreading at a rate of 17% per week, while begins with 22 people. What equation or expression should be used? Also, how many people will be infected after 28 weeks?

Question

(N represents the number of weeks.)

PLEASE HELP! (My teacher assigned it as homework, but I have no idea what to do.)

Answer 1

This is similar to compound interest. If the number of people infected is P to start with (P=22 in this case) then after one week the number of people infected is P(1+r), where r is the rate of infection (=17% or 0.17 in this case). At the end of the second week, the number of people infected rises to P(1+r)(1+r)=P(1+r)^2. After the third week it's P(1+r)^3 and so on. After N weeks it's P(1+r)^N. After 28 weeks it's 22*(1.17^28)=22*81.134=1785 people.

Comments

Thank you so much!