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Nicholas sent a chain letter to his friends, asking them to forward the letter to more friends. Every 12
weeks, the number of people who receive the email increases by an additional 99%, and can be modeled
by a function, P, which depends on the amount of time, t (in weeks).
Nicholas initially sent the chain letter to 50 friends.
Write a function that models the number of people who receive the email t weeks since Nicholas initially
sent the chain letter.
P(t) =?

Respuesta :

Answer:

[tex]P(t)=50(1.99)^{t/12}[/tex]

Step-by-step explanation:

The problem can be modeled by using the compound growth formula.

Given, Initial number [tex]P_0[/tex] of people who Nicholas sent the chain letter to=50

The growth rate, r =99%=0.99

Period of Growth,k =12 Weeks

[tex]P(t)=P_0(1+r)^{t/k}[/tex]

Therefore, in any week (t) after Nicholas initially sent the mail, the number of people who receive the email is modeled by the function:

[tex]P(t)=50(1+0.99)^{t/12}\\P(t)=50(1.99)^{t/12}[/tex]

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