Your friend sends out a chain letter e-mail to 12 people and by the next day 15 people have received the letter. Assuming an exponential growth pattern, how many new people will receive it by the 30th day?
If by "new" you mean all except the original 12, then
12((15/12)^30 - 1)
Extra credit: how many people receive it on the 30th day?
To determine the number of new people that will receive the chain letter by the 30th day, we need to understand how exponential growth works in this scenario.
Exponential growth occurs when a quantity increases at a fixed percentage rate over a set period of time. In this case, the number of people receiving the chain letter is doubling each day.
We know that on the first day, 12 people received the letter. By the second day, 15 people received it. This means that the number of people receiving the letter is increasing at a rate of 3 people per day (15 - 12 = 3).
So, every day the number of people receiving the letter is doubling, and the initial number of people is 12.
To find out how many new people will receive the letter by the 30th day, we can use the formula for exponential growth:
N = P * (2^d)
Where:
N is the final number of people receiving the letter,
P is the initial number of people receiving the letter,
d is the number of days.
Plugging in the values, we have:
N = 12 * (2^30)
Calculating this value will give us the answer.
To determine the number of new people who will receive the chain letter by the 30th day, we need to use the exponential growth formula:
N = N₀ * (r^t)
Where:
- N is the final number of people who received the letter
- N₀ is the initial number of people who received the letter
- r is the growth rate
- t is the time in days
In this case:
- N₀ = 12 (initially 12 people received the letter)
- N is what we want to find
- t = 30 (we want to find the number of new people by the 30th day)
We know that by the next day, 15 people have received the letter, so we can calculate the growth rate (r):
15 = 12 * (r^1)
Simplifying the equation:
r = 15/12
r = 1.25
Now we can use the growth formula to find the number of new people who will receive the letter by the 30th day:
N = 12 * (1.25^30)
Using a calculator, we find:
N ≈ 39,477
Therefore, approximately 39,477 new people will receive the chain letter by the 30th day.