Question

Jane writes a chain email and sends it to five friends. If each person who receives the email reads it within 5 minutes of the email arriving and then sends it to five other people. If the email always goes to a new person and assuming every person in Australia has read the message . How long would it take until everyone in Australia has read the email?

Answer 1

Assuming that everyone who receives the email forwards it to exactly five other people who have not yet received it, we can use a simple exponential growth formula to estimate how long it would take for the entire population of Australia to receive the email:

N = 5^x

where N is the total number of people who have received the email after x rounds of forwarding. Initially, the email is sent to 5 people, so N = 5 when x = 0.

We want to find the value of x when N is equal to the population of Australia, which was approximately 25.7 million people in 2021. So we can set up the following equation:

25.7 million = 5^x

Taking the logarithm of both sides, we get:

x log(5) = log(25.7 million)

Solving for x, we get:

x = log(25.7 million) / log(5)

x ≈ 8.56

Therefore, it would take approximately 8.56 rounds of forwarding for the email to reach every person in Australia. Since each round of forwarding takes 5 minutes, the total time it would take for everyone in Australia to receive the email would be:

8.56 rounds x 5 minutes per round = 42.8 minutes

So it would take about 42.8 minutes for the email to reach every person in Australia, assuming everyone who receives the email forwards it to exactly five other people who have not yet received it.

Answer 2

Answer: If each person who receives the email sends it to five other people, the number of people who receive it multiplies by five each time the email is forwarded. Therefore, the number of people who receive the email after n iterations are given by:

5^n

Initially, the email is sent to five people, so after the first iteration, 5^1 = 5 people have received the email. After the second iteration, 5^2 = 25 people have received the email. After the third iteration, 5^3 = 125 people have received the email. And so on.

We want to know how many iterations it will take for the email to reach everyone in Australia. According to the Australian Bureau of Statistics, the population of Australia was approximately 25.7 million people in 2021. Therefore, we need to solve the equation:

5^n >= 25,700,000

Taking the logarithm of both sides, we get:

n*log(5) >= log(25,700,000)

n >= log(25,700,000) / log(5)

n >= 7.9

Therefore, it will take at least 8 iterations for the email to reach everyone in Australia. Since each iteration takes 5 minutes, the total time it will take for everyone in Australia to read the email is:

8 iterations x 5 minutes per iteration = 40 minutes.

So, it will take 40 minutes for everyone in Australia to read the email, assuming every person who receives the email forwards it to five new people who have not yet received it.

Explanation: