Derek sent a chain letter to his friends, asking them to forward the letter to more friends. The group of people who receive the email gains 9/10 of its size every week and can be modeled by a function, P, which depends on the amount of time, t (in weeks).
Derek initially sent the chain letter to 40 friends.

Write a function that models the group of people who receive the email t weeks since Derek initially sent the chain letter

A function that models the group of people who receive the email t weeks since Derek initially sent the chain letter is p(t) =[tex]40 + 12t[/tex] (in t weeks).

What is a function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The number of people who received letters three weeks later:

= [tex]40 + \frac{9}{10} \times40[/tex]

= [tex]76[/tex]

The number of people who received letters one week later:

= [tex]40+(\frac{9}{10} \div3)\times40[/tex]

= [tex]52[/tex]

The number of people who received letters t week later:

= [tex]40+(\frac{9}{10} \div3).t\times40[/tex]

= [tex]40 + 12t[/tex]

So, a function that models the group of people who receive the email t weeks since Derek initially sent the chain letter is p(t) = [tex]40 + 12t[/tex] (in t weeks).

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