A plague infects ten people. Every day, each infected person infects six others. How many people are infected after three days?
Answer: After three days, 2710 people are infected.
Step-by-step solution
Step 1: Calculate new infections on Day 1
We start with 10 initially infected people. On the first day, each of these 10 people infects 6 new individuals. To find the number of newly infected people on Day 1, we multiply the initial number of infected people by the infection rate per person.
Step 2: Calculate total infected after Day 1
The total number of infected people after Day 1 is the sum of the initially infected people and the newly infected people on Day 1. This gives us the base for calculating infections on subsequent days.
Step 3: Calculate new infections on Day 2
On Day 2, all the people who were infected by the end of Day 1 (initial + new) will infect others. We multiply the total number of infected people after Day 1 by the infection rate to find the new infections on Day 2.
Step 4: Calculate total infected after Day 2
To find the total number of infected people after Day 2, we add the people who were already infected by the end of Day 1 to the new infections that occurred on Day 2.
Step 5: Calculate new infections on Day 3
On Day 3, all the people who were infected by the end of Day 2 infect others. We multiply the total number of infected people after Day 2 by the infection rate to find the new infections on Day 3.
Step 6: Calculate total infected after Day 3
Finally, to find the total number of infected people after three days, we add the people who were infected by the end of Day 2 to the new infections that occurred on Day 3.