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Nicholas sent a chain letter to his friends, asking them to forward the letter to more friends. Every 121212 weeks, the number of people who receive the email increases by an additional 99\%99%99, percent, and can be modeled by a function, PPP, which depends on the amount of time, ttt (in weeks).

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Edufirst

Answer:

Since the question is incomplete, see below for a fully understanding of this kind of questions.

Explanation:

The question is incomplete but you can set some assumptions and determine the function that model the situation.

The relevant data of the text are:

  • Every 12 weeks, the number of people who receive the email increases by and additional 99%

From that you can:

  • determine the growing factor
  • determine the function P, which depends of the amount of time t (weeks) and models the function

Solution

You can build a table or write a sequence to help you to figure out what is going on:

First, you need to know the number of friens to whom NIcholas initially sent the chain letter. You must assume a number. Assuming Nicholas initially sent the chain letter to 10 frirends, this would be the table:

t (weeks)       P(t)

0                    10

12                   10 + 99% of 10 = 10 + 0.99× 10 = 10 (1.99)

24                   10(1.99)(1.99) = 10 (1.99)²   ↔ two times 12 weeks

36                   10(1.99)³                             ↔ three times 12 weeks

This is every 12 weeks the number of people who recieve the email is multiplied by 1.99.

That means that the grow factor is 1.99 every 12 weeks, and the power of the exponential function is the number of 12 weeks elapsed, which is t divided by 12: t/12

           [tex]P(t)=10(1.99)^{(t/12)}[/tex]

It is important that you realize that t/12 means the number of times that 12 weeks elapse.

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