Final answer:
To find the number of people who receive the letter, multiply the starting number by 5 raised to the number of steps taken. The number of people who don't send out the letter is the total number of people who sent it out minus the number of recipients. Hence 3125 received it, and 6875 people did not send it out.
Step-by-step explanation:
To find the number of people who receive the letter, we can keep track of each step in the chain. The first person sends the letter to five others, so there are now 5 people who have received it.
The next step, each of these 5 people can either send it to 5 new recipients or not send it at all. If they send it, that's 5 x 5 = 25 new recipients. If they don't, the number of recipients stays the same at 5.
Continuing this process, we can see that each step multiplies the number of recipients by either 5 or 1.
Since the chain ends after 10000 letters have been sent, we can determine the number of recipients by finding the number that gets multiplied by 5^k, where k is the number of steps taken.
Let's calculate how many steps we need to reach 10000 recipients: 5^k = 10000. Taking the logarithm of both sides, we get k = log(10000) / log(5)
= 4.
To find the number of recipients, we simply multiply the starting number (5) by 5^k.
So the number of recipients is 5 x 5^4 = 5 x 625
= 3125.
To find the number of people who don't send the letter out, we can subtract the number of recipients from the total number of people who sent out the letter.
If 10000 people sent out the letter, and 3125 received it, then 10000 - 3125 = 6875 people did not send it out.