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Tobias sent a chain letter to his friends, asking them to forward the letter to more friends. The number of people who receive the email increases by a factor of 4 every 9.1 weeks, and can be modeled by a function, f(p) which depends on the amount of time, t (in weeks). Tobias initially sent the chain letter to 37 friends. Write an exponential function describing this scenario. Use "^" to denote an exponent and "/" to denote a fraction sign.

Respuesta :

Edufirst

Answer:

  • [tex]P(t)=37\times (4)^{(t/9.1)}[/tex]

Explanation:

The number of emails is multiplied by 4 every 9.1 weeks.

Thus, since Tobias initially sent the chain letter to 37 friends, the number of letters will grow as per this geometric series:

Start:        37 letters

  • In 9.1 weeks: 37 × 4

  • In 2 × 9.1 weeks: 37 × (4)²

  • In 3 × 9.1 weeks: 37 × (4)³

As you see, the exponent is the number of weeks divided by 9.1

Thus, if your variable is the number of weeks, t, then the exponent is t/9.1

And the exponential function, P(t) will be:

   [tex]P(t)=37\times (4)^{(t/9.1)}[/tex]

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